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- Permanent Link:
- https://ufdc.ufl.edu/UF00084177/00001
Material Information
- Title:
- A computerized method of evaluating trace particle records of turbulent flow fields
- Creator:
- Jackman, Gary Ralph, 1945-
- Publisher:
- University of Florida
- Publication Date:
- 1976
- Language:
- English
- Physical Description:
- vii, 149 leaves : ill. ; 28 cm.
Subjects
- Subjects / Keywords:
- Cinematography ( jstor )
Computer programs ( jstor ) Coordinate systems ( jstor ) Data acquisition ( jstor ) Flow distribution ( jstor ) Movies ( jstor ) Reynolds number ( jstor ) Velocity ( jstor ) Velocity distribution ( jstor ) Writing tablets ( jstor ) Dissertations, Academic -- Engineering Sciences -- UF Engineering Sciences thesis, Ph.D. Turbulence -- Data processing ( lcsh )
Notes
- Thesis:
- Thesis--University of Florida.
- Bibliography:
- Bibliography: leaves 145-148.
- General Note:
- Typescript.
- General Note:
- Vita.
- Statement of Responsibility:
- by Gary Ralph Jackman.
Record Information
- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Gary Ralph Jackman. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 025800585 ( ALEPH )
03334552 ( OCLC ) AAV1826 ( NOTIS )
Aggregation Information
- UFIR:
- Institutional Repository at the University of Florida (IR@UF)
- UFETD:
- University of Florida Theses & Dissertations
- IUF:
- University of Florida
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A COMPUTERIZED METHOD OF EVALUATING TRACE PARTICLE RECORDS OF TURBULENT FLOW FIELDS
By
GARY RALPH JACKMAN
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1976
ACKNOWLEDGMENTS
I wish to express my gratitude to Professor E. Rune Lindgren,
my supervisory chairman, for his guidance throughout this work. His enthusiastic support and technical assistance were invaluable. Special thanks for the many hours devoted to the written work of an inexperienced author. I wish to thank Dr. Kurzweg for his stimulating support and advice on a near daily basis. I would like to thank Dr. Boykin for his overall interest and in particlular for his help with digital filtering. I would also like to express my thanks to Drs. Keefer and Roan for their encouragement and assistance.
My thanks go to Dr. Elkins for his help and friendly criticism
during most phases of this work. I thank Dr. Yoo for his work with the Pictorial Data Acquisition Computer and associated computer programs. My thanks go to Randall Crowe who spent much time helpinA apply the data tablet method of digitizing to this work and helping me while I learned to program. Special thanks to Terry Lapinsky, who typed this dissertation.
Words fail to express my appreciation to these people who helped so much.
This work was supported in part by the National Science Foundation under Grant No. ENG75-03470 and in part by the Office of Naval Research under Grant No. N00014-75-C-1090.
TABLE OF CONTENTS
ACKNOWLEDGMENTS.; . LIST OF FIGURES . ABSTRACT.
CHAPTER
1 INTRODUCTION .
1.0 Techniques for Measuring Turbulence .
1.1 The Problem and the Proposed Solution .
2 EXPERIMENTAL ARRANGEMENT .
2.0 Introduction .
2.1 Pipe Flow Apparatus .
2.2 Data Acquisition Equipment .
3 METHOD OF DATA ACQUISITION .
3.0 Introduction .
3.1 Trace Particle Method of Flow Visualization.
3.2 Prism Analysis and Calibration.
3.3 Operation of the Experimental System .
4 METHOD OF DATA REDUCTION .
4.0 Introduction .
.4.1 Pictorial Data Acquisition Computer Method .
4.2 Data Tablet/Digitizer Method .
4.3 Method of Following Particle Images and
Matching Image Pairs .
Page
ii
v
vii
4.4 Method for Determination of Three Dimensional Positions and Velocities . 57
4.5 Referencing Data to a Grid . 75
4.6 Method for Displaying Reconstructed
Flow Fields . 81
4.7 Comments . 97
5 THE STRUCTURE OF TURBULENCE AT LOW REYNOLDS
NUMBERS . 103 5.0 Introduction . 103 5.1 Digital Filter Cutoff Frequency Determination. 103
5.2 Observations of Pipe Flow in the Transition
Zone . i11
5.3 The Experimental Results of the Pipe Flow at
a Reynolds Number of 3500 . 115
6 SUMMARY AND CONCLUSIONS . 125
6.0 Summary of the Data Acquisition and
Evaluation . 125
6.1 Conclusions of the Data Acquisition and
Evaluation . 133
6.2 Summary of the Investigation of Turbulence
at Low Reynolds Numbers . 134
6.3 Conclusions of the Investigation of Turbulence
at Low Reynolds Numbers . 137 APPENDIX A DERIVATION OF THE RELATIONSHIP BETWEEN THE
IMAGE POSITIONS AS VIEWED IN TWO FACES OF A
PRISM AND THE PARTICLE POSITION IN A PIPE . 139 BIBLIOGRAPHY . . 145 BIOGRAPHICAL SKETCH. 149
Chapter
Page.
LIST OF FIGURES
Figure Page
2.1 Experimental pipe flow apparatus . 15
2.2 Data acquisition section of pipe (test section) . 16
2.3. Relationship of the apex of the viewing volume
to prism size . 17 3.1 Prism, pipe, and camera . 27 3.2 Prism arrangement with field of view in flow . 28
3.3 Prism and pipe . . . . 29 4.1 Flowchart of the method of data reduction . 32
4.2 Computer program for converting data tablet coded
coordinates to referenced X-Y coordinates . 39
4.3 The particle image series startup process . 48
4.4 Computer program for following image positions and
matching image pairs . 49
4.5 Computer program to calculate filtered positions
and velocities . 65 4.6 Computer program to rearrange data by frame . .74
4.7 Computer program to reference velocity field to
known locations . 78 4.8 Three dimensional velocity field . 85
4.9 R-O plane segment velocity fields . 86
4.10 X-R plane segment velocity fields . 87
4.11 Three dimensional particle path display . 88
4.12 Computer program to construct velocity fields . 89
4.13 Computer program to construct particle path
display . 95
Figure Page
5.1 Position error vs. frequency . 109 5.2 Velocity error vs. frequency . 109 5.3 Flow RMS velocity vs. cutoff frequency . 110 5.4 Change in radial RMS velocity vs. cutoff frequency. 110
5.5 Average axial velocity vs. distance from pipe wall. 122
5.6 Root-mean-square velocities vs. distance from
pipe wall . 123 5.7 Mean-velocity distribution . 124 A-1 Prism, pipe, and camera . 143 A-2 Prism and pipe . 144
Abtract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
A COMPUTERIZED METHOD OF EVALUATING TRACE PARTICLE RECORDS OF TURBULENT FLOW FIELDS By
Gary Ralph Jackman
December 1976
Chairman: E. Rune Lindgren
Major Department: Engineering Sciences
In a Ph.D. dissertation at the University of Florida in 1974,
Johnson used a prism to view particles tracing the motion of fluid in a pipe. The particles viewed in the prism were recorded with a cinematographic camera. The prism produces two images for each particle, and geometric relationship uniquely determines the true particle position from the two image positions. Starting from Johnson's manual method, computerized evaluation techniques have been developed to digitize the cinegraphic records of the flow entrained trace particles. The digitized data are processed through computer programs developed to follow the recorded particle images as they traverse the prism faces and pair the image paths that correspond to particles traversing the studied flow volume. These data are further processed to yield three dimensional positions and velocities. Computer-graphic methods are developed and used to display the instantaneous flow in two or three dimensional views.
CHAPTER I
INTRODUCTION
1.0 Techniques for Measuring Turbulence
The study of the structure of turbulence is a problem which has attracted the collected efforts of the scientific community for more than 100 years. The difficulties have stimulated the development of a variety of techniques which have been used with varying degrees of success and range from the simple qualitative but very informative trace-dye observations by Reynolds, 1883, to the quantitative, sophisticated laser measurements of today.
Anemometer probes which are inserted into flow fields to measure average and fluctuating velocities record changes in electrical, chemical, or mechanical probe parameters caused by the fluid flowing next to the probe. Besides the requirement that the measuring probe must cause a minimum of interference with the flow field, there are a number of specific restrictions for this type of equipment to be used successfully in measuring turbulence. Some of the crucial requirements have been listed by Hinze, 1975. The probe must be as small as possible in order to minimize flow field distortions induced by it. There must not be a velocity gradient in the region of the probe sensor therefore the sensor must be smaller than the dimension of the smallest turbulent "eddies". (The smallest length scale of the turbulence is 0.25 mm at Re = 8000 and 0.8 mm at Re = 2200 in a 12.7 cm diameter pipe. The Reynolds number is Re = U D/v where U is the average pipe flow
velocity, D is the diameter of the pipe, and v is the kinematic viscosity.) The inertia of the instrument must be low enough for it to respond to the highest frequencies encountered in the turbulent flow. The sensing element must be sufficiently rigid to prevent flow induced vibrations while being sensitive enough to detect the very small fluctuations of velocity which are typically a few percent of the average flow velocity. The probe anemometer system must be stable enough to exclude calibration shifts during a test run. All these restrictions are very difficult for probe anemometer instruments to satisfy since they require the probe to be large for rigidity but small for minimizing flow interferences and avoiding velocity gradient distortions.
Up to the present, the hot-wire and hot-film anemometer's development and application for quantitative measurements of turbulent flow have by far surpassed all other probe anemometers for use in gases and liquids. The vast bulk of quantitative information about the structure of turbulence has been obtained using these anemometers. The sensing elements of the hot-wire and hot-film anemometer are heated by electric current and cooled by the fluid flowing around them. The total heat transfer depends on 1) the flow velocity, 2) the difference in temperature between the fluid and the wire, 3) the physical properties of the fluid, and 4) the dimensions and physical properties of the wire. At present the constant-temperature anemometer is used almost exclusively. Here the electric resistance of the sensing element and, consequently, the temperature are kept constant with the cooling by the flow being compensated for by an increase in electric current. The operation of the hot-wire anemometer is described in detail by Hinze, 1975. The turbulent intensity must be small compared to the average flow velocity
in order for a linearization of the hot-wire response to turbulent fluctuations to be valid. Errors of up to 10% may be found for turbulent intensities of 20%. Wygnanski, Sokolov, and Friedman, 1975, recorded turbulent intensities exceeding 20% of the average flow velocity within the transition range of Reynolds numbers for pipe flow. Johnson, 1974, recorded axial turbulent intensities 15% of the average flow velocity at Reynolds numbers of 4000, 6500, and 9000 in a 12.7 cm diameter pipe. According to Perry and Morrison, 1971 a and b, errors up to 20% may be associated with the usual static calibration procedures and up to 20% difference in turbulent intensity may be recorded by different anemometer systems in the same flow. Even with the calibration complete and the above mentioned errors known, there are additional problems associated with the hot-wire and hot-film systems. The calibration can shift with impact or deposit of contaminants on the sensing element. Changes in the wire properties can occur due to excessive temperatures. According to observations by Johnson, 1974, hot-film calibration data indicate the existence of a critical velocity value below which the hot-film probe is insensitive to velocity change close to the flow boundaries. The probe size and thermal interferences restrict the proximity of the probe placement to a boundary. It is noteable that the hot-wire and hot-film anemometers can only measure one or two components of velocity at a single location for each probe.
A more sophisticated system used for flow studies is the Laser
Doppler Anemometer (LDA) which was first used by Yeh and Cummins, 1964. Here the fluid velocity is determined by recording the Doppler shift of the scattered laser light beam. The scattering is caused by particles entrained in the flow which traverse the measuring section. The anemometer
consists of a laser, a beam splitter, a light collector, a photodetector, and a signal processor. The advantages are that there is no probe and no flow calibration is required. The Laser Doppler Anemometer measures the flow velocity within a volume which is usually somewhat larger than the linear dimensions of a hot-film probe. Noise is generated by a mean velocity gradient in the measuring volume when particles traverse different sections of the measuring volume at different velocities. Noise is also generated by phase and amplitude variations in the Doppler shift from multiple particles traversing the measuring volume at the same time. Thus, low particle densities are necessary. Laser systems are very expensive. It is a difficult task to focus the crossed laser beams and to determine the location of the measuring volume in a pipe. Two crossed beams allow only one component of velocity to be determined and at only one location at a time.
Some other techniques for studying turbulence utilize various means of making the flow visible to a detecting apparatus outside of the flow field. These techniques run the spectrum from qualitative through quantitative observations. The discussion is limited to methods which make the flow of liquids visible. The methods utilize discrete particles called trace particles or-continuous"materials such as dyes, powders, or birefringent solutions.
The transition experiments done by Reynolds, 1883, utilized tracedye to visualize the intermittency of the onset of turbulence in pipe flows. The first experiments using aluminum powder on free surfaces of water for studying channel flows were done by Ahlborn, 1902. Prandtl and Tietjens, 1934, used this same technique in their experiments on flow around cylinders and airfoils. Prandtl, 1904, suspended small
5.
flakes of mica in water to visualize regular motions since a large number of flakes would orient themselves to the flow direction. Binnie and Fowler, 1947, and Lindgren, 1954-1969, studied the transition process in pipe flows of water by addition of birefringent colloidal suspensions, viewing the flow by means of crossed polarization sheets. This technique is very sensitive for the discrimination between laminar and turbulent flow but does not allow any quantitative measurements of the structure of turbulence. Similar observations can be made by mixing aluminum powder in the flow as done by Coles, 1965. These are but a few of the many continuous or near continuous flow visualization methods that have been used to visualize the flow of liquids. They are all limited to qualitative information or, at best, some gross quantitative information.
Another flow visualization technique is the hydrogen bubble method which was first described by Kolin, 1953. Clutter, Smith, and Brazier, 1961, applied this technique to the study of flow around aircraft models. Schraub, Kline, Henry, Runstadler and Littell, 1965, achieved a major advancement in the use of the hydrogen bubble technique for quantitative studies by pulsing the voltage and insulating spanwise portions of the wire to produce combined time-streak markers. Schraub et al., 1965, give a detailed description of the measurement of velocity using the hydrogen bubble technique and an error analysis of the velocity. Kline, Reynolds, Schraub, and Runstadler, 1967, and Kim, Kline, and Reynolds, 1971, made use of this technique for obtaining qualitative and quantitative information on turbulence in a boundary layer. The hydrogen bubble technique is limited to low speeds and low frequency turbulent fluctuations. Only one component of velocity at several locations along
the electrode can be determined at a time. Kline and his coworkers calculated the fluctuations in velocity by subtracting the hydrogen bubble determined instantaneous velocity from long time averaged hotwire anemometer readings of velocities. Kim et al., 1971, state that the accuracy of the data and particularly of the fluctuations is low for this technique. A serious limitation of this method is the bouyancy of the bubbles which will cause them to rise relative to the flow pattern they supposedly should record.
The use of discrete particles for flow visualization is also a
well known technique for flow visualization. A method for making spheres with a specific gravity very close to water was reported by Marey, 1893. The spheres were a mixture of wax and rosin for use as trace particles in water. Eden, 1912, injected oil into the fluid by means of an atomizer and illuminated a thin sheet for visualization of the fluid flow. Fage and Townend, 1932, used their ultramicroscope to measure motions close to the wall of a pipe by observing dust particles naturally abundant in the water. Van Meel and Vermij, 1961, obtained three dimensional position components by using a number of layers of different colored light stacked normal to the photographic plane. A color photograph was taken and the component of position normal to the plane was known to the limit of the thickness of the color layer. Nedderman, 1961, used two cameras placed at an angle to each other to simultaneously photograph small air bubbles to obtain three dimensional positions and velocities near the wall in turbulent pipe flow. Nieuwenhuizen, 1964, used a set of mirrors to put a front and side view of the particles in the flow on one camera frame. Corino and Brodkey, 1969, used colloidal sized particles of magnesium oxide suspended in trichloroethylene which
was the experimental fluid. High speed motion pictures were taken of a very thin planer section as the camera was transported downstream. Nychas, Hershey, and Brodkey, 1973, used pliolite trace particles in water in the same apparatus as Corino and Brodkey, 1969.
Johnson, 1974, introduced a prism for studying the motion of pliolite trace particles in the flows of water through pipes. This technique permits determination of the three dimensional position of each particle in the flow field viewed through the prism. The prism produces two images for each particle and a geometric relationship uniquely determines the true particle position from the two image positions. There is no probe to disturb the flow field. The particles are almost neutrally bouyant and are chosen small enough to follow the fluid motion very closely. Recording the image positions by means of a frequency monitored cinematographic camera then permits a quantitative as well as a qualitative three dimensional reconstruction of the studied flow field and its variation in time. The changes in particle position can be progressively more precisely followed by using a higher film rate (frequency) to record them. No calibration is required and the data recording cannot shift if the equipment is undisturbed. The prism/ trace particle method seems potentially to be superior to any other technique presently in use to describe the instantaneous characteristics of flow fields and seems to imply a major step forward in the field of experimental fluid dynamics. As far as this author knows, this is the only method of acquiring a quantitative record of an entire flow volume simultaneously through time.
1.1 The Problem and the Proposed Solution
The problem now is to implement the data in the record of observations
in order to utilize the potential of Johnson's prism/trace particle method. This necessitates some kind of automation of the processing of the cinematographic records. The sheer volume of stored data prevents any manual evaluation of the records should all the information stored be utilized for analysis of the three dimensional flow field. The present work is limited to the development of techniques for numerical reconstruction of the three dimensional flow field being studied, including automated processes for its graphical display in a variety of fashions. It should be mentioned that the present method of data reduction can be used with very little modification to process the data contained in the records of the experiments by Nychas, Hershey, and Brodkey, 1973. Because of the magnitude of manual work required they could not previously evaluate these data quantitatively.
The method of data acquisition described by Johnson, 1974, has
been used with only slight modifications. The cinematographic records of the flow entrained trace particles have been translated into digital data by two methods. In the first method, a Pictorial Data Acquisition Computer (PIDAC) is utilized. It automatically scans light which passes through the motion picture film and records the light intensity level at various locations on the film. This information is thereafter processed to yield the digitized location of each particle image. In the second method, a Scriptographics data tablet/digitizer is utilized. Each cinematographic frame is enlarged and displayed on the tablet for digitization one by one. The translated data from both methods has been processed through computer programs that developed to follow particle images as they traverse the experimental area on the prism faces and pair the image paths that correspond to particles traversing the studied flow
9
volume. These data were further processed to yield true positions and velocities. Computer graphics methods have been developed and used to display the instantaneous flow field in two and three dimensional views.
CHAPTER II
EXPERIMENTAL ARRANGEMENT
2.0 Introduction
The experimental equipment used for this work is located in the Fluid Mechanics Laboratory of the Engineering Sciences Department at the University of Florida. It consists of two parts: the constanthead, closed circuit pipe flow apparatus which uses water as its experimental fluid; and the prism arrangement or the data acquisition apparatus which consists of a prism, a light source, and a movie camera.
2.1 Pipe Flow Apparatus
The flow apparatus, equipped for flow studies by means of the
prism/trace particle method, is shown in Figure 2.1. The first of its components, the constant-head overflow tank (1), is simply an open topped container within a container. The fluid is routed to the containers through a polyvinyl chloride pipe from the pump (7). The flow must be slightly greater than the flow through the test pipe (3) in order to ensure a constant head on the system. The inner container is thus kept full with the excess fluid overflowing into the outer container which drains into the mixing tank (8). The fluid in the inner container travels down the third polyvinyl chloride pipe to the settling chamber (2) where it passes through a honeycomb rectifier. The fluid then passes around a flat plate perpendicular to the flow with approximately two millimeters of clearance thus ensuring a thorough mixing of the fluid at the entrance of the test pipe (3).
The test pipe (3) is a 23.6 meter long plexiglass pipe. of 127 mm inside diameter. The test pipe was carefully aligned both longitudinally and horizontally to ensure a straight horizontal test section. It has eleven permanent joints and five flanged, o-ring-sealed joints which were carefully matched. The inside diameter of the test pipe was checked and found to vary by less than + 0.5 mm. The data acquisition equipment is located in the section of the test pipe farthest downstream, labeled (3a) in Figure 2.1. The fluid exits the test pipe through a plexiglass access chamber (4), whose dimensions are 0.45 meters in length and .203 meters in diameter. A mount for a hot-film anemometer probe and a mirror to reflect light from a light source up the test pipe parallel to the longitudinal axis are installed in the access chamber. There is also a thermometer to monitor the fluid temperature.
The flow exits the access chamber, passes through the return line
(5) which is a 75 mm inside diameter plexiglass pipe, and reverts to the pump to be recycled through the system. Two Ramapo Mark V turbulent drag type flowmeters (models V-3-SP and V-l-SP) each upstream of a regulating valve are located in the return line. The two flowmeters and regulating valve systems (6) are arranged in parallel, which allows the use of either system. The Mark V-3-SP has a range of 0.0013 to 0.013 m3/s for high Reynolds number flows and the Mark V-l-SP has a range of 0.00013 to 0.0013 m3/s for low Reynolds number flows. This arrangement allows accurate measurements over a wide range of flow rates. The strain gauge in the Mark V-l-SP flowmeter is connected to a Wheatstone bridge and a Sola DC power supply. The output is connected to a Honeywell Electronik 194 potentiometric strip chart recorder and a Hewlett Packard Model 412 DC vacuum tube voltmeter. The flow measuring unit was calibrated
by the bucket, scale, and stopwatch method with a minimum of four replications of every reading with less than 0.5% error. The scale was a Detecto floor scale which was checked by three different methods for accuracy. Downstream of the flowmeters, the fluid exits the return line into the pump. The pump (7) is a glass lined Gould centrifugal machine with a maximum flow rate of 0.013 m3/s at 10 m water overhead pressure. It has a flexible connection with the return line in order to insulate the flow in the pipe from mechanical vibrations of the pump.
The mixing tank (8) is connected to a storage tank (9) and the overflow from the constant-head tank (1). The fluid i n the mixing tank maintains a constant pressure on the upstream side of the pump (7) which helps prevent cavitation in the pump. The constant pressure i n the mixing tank also maintains a constant pressure on the return line so as to ensure steady flow conditions in the test pipe (3).
Two cooling elements are located in the system to maintain a constant temperature throughout the operating time for an experimental run since the pump and the ambient conditions add energy to the system thus attempting to elevate the temperature of the fluid. One is a Precision Scientific Company portable cooler with its cooling element located in the constant-head tank (1). This cooler is not fluid temperature regulated. The other is a Blue M 250 W cooler with its cooling element and sensor located in the mixing tank (8). This is a variable setting fluid temperature regulated cooler.
The water used as the experimental fluid is from the city water supply. In order to ensure that the water is clean, an Aqua-Pure water filter model P10-1 was installed on the city water tap. Six deaerating taps allowed for the elimination of entrapped air in the experimental system. Of the six, four taps are manually regulated. Two of these
manually regulated taps are located on the test pipe (3); one is situated on the access chamber (4); and one tap is on the return line (5). The two remaining taps are open bleed taps. One open bleed tap is located in the settling chamber (2), and the other is situated in the mixing chamber (8). The chlorine in the city water supply cannot attack the system since all metal parts are fiberglass coated except the Ramapo flowmeters which are stainless steel.
2.2 Data Acquisition Equipment
The data acquisition equipment (located at 3a in Figure 2.1) is shown in Figure 2.2. The light source is a Beseler slide projector with a 750 W bulb. The collimated beam from the projector is reflected by a mirror aligned 450 to both the projector and the flow. This allows the beam to pass through the prism viewing volume and parallel to the flow. The end of the test pipe was painted black to prevent the light from traveling in the plexiglass pipe which would raise the level of the background light intensity. A 35 mm model 71 Bell and Howell movie camera was used to film the pliolite trace particles in the fluid as seen through the two faces of the glass prism.
Two glass prisms mounted side-by-side were used in this work. The first prism is the same one used by Johnson, 1974, in his dissertation work. It is a 68 mm base, 900 prism, 56 mm long. Figure 2.3 shows that the apex of the viewing volume is just prior to the centerline of the pipe. This is satisfactory for turbulent flow at low Reynolds numbers but it was felt that for transition flow, the apex of the viewing volume should be such that a large area in the vicinity of the centerline of the pipe is in view. For this reason, another prism was mounted on the test pipe. The larger prism is a 113 mm base, 160 mm long, 900 crown glass
prism made by Ealing Optics Company. This prism has the apex of its viewing volume greater than two pipe diameters from the pipe wall/ prism in water. A complete analysis of the prism and pliolite trace particle method will be developed in Chapter III.
To have a complete acquisition of data, the movie frames must have a reference point to locate the axial coordinate origin and two reference points to line up the prism vertical. The frame rate or film speed must also be known. The referencing is accomplished by using two wheat grain bulbs of low light intensity which are reflected off the prism to give two reference spots aligned with the pipe axis. One spot will define the horizontal position of the frame and the two together will define the rotation or misalignment of the frame. The frame rate is acquired by filming a Hewlett Packard 5243L electronic counter.
L�i]
1 - Constant-head overflow tank 5 - Return pipe
2 - Settling chamber 6 - Flowmeters and
3 - Test pipe regulating valves
3a - Data acquisition section 7 - Pump
4 - Access chamber 8 - Mixing tank
9 - Storage tank
FIGURE 2.1 Experimental pipe flow apparatus
Prism Castor oil
Pipe
FIGURE 2.2 Data acquisition section of pipe (test section)
113 mm
68 mm
Large Pri sm
A I
~ t I
4
I I
/
I
\ I/
\ /i
V
Apex of the viewing
volume for
small prism
Apex of the viewing
volume for
large prism
FIGURE 2.3 Relationship of the apex of the viewing volume to prism size
,v \ Small Prism
/
I
P
CHAPTER III
METHOD OF DATA ACQUISITION
3.0 Introduction
The data acquisition phase consists of all steps required to
cinematographically record the flow field pattern. This is accomplished by adding trace particles to the fluid and photographing the flow using a method that will relate the cinematographic film to the three dimensional flow field. The method of data acquisition used in this work was first developed by Johnson, 1974. It employs pliolite particles as the flow visualization material and a prism to relate the two dimensional cinematographic film to the three dimensional pipe flow. The method will be developed in three parts. The first part will develop the trace particle method flow visualization. This will be followed by the prism analysis and calibration. Lastly, the operation of the data acquisition apparatus and the experimental flow apparatus will be discussed.
3.1 Trace Particle Method of Flow Visualization
The trace particles used in this method of flow visualization are pliolite supplied by Goodyear Chemicals, Akron, Ohio. The pliolite, pebble sized when received from the supplier, was ground in a colloidal mill and sieved to yield particles of 48 to 63 pm in size. These particles were then mixed in water and left for 24 hours. The particles that settled and the particles that floated were removed. The water with the neutrally buoyant particles was added to the system through the constant-head tank. It was decided to try adding the particles to the system without going
through the tedious and time consuming task of mixing and letting the mixture stand. Within one hour, the particles from both methods acted in similar fashion in the flow system. The density of pliolite is
1.026 g/cm3. The particles responded the same whether mixed in water or dry when added to the system. The particles selected were small enough to follow closely the fluid motion and large enough to be photographed with a movie camera under the available lighting. Johnson justifies the use of the pliolite particles in a lengthly argument (Johnson, 1974, pp. 38-39) which will not be repeated here, although a comment on this analysis seems appropriate. Johnson uses the equation,
U' (TL + 2)
U' OTL + 1)
00
where a= (p36 ) d2 = , T= Lagrangian time scale =fRL(T)dT,
(2 +P)(2p + p) L
whep
U' is the root-mean-square value of the particle motion, U' is the rootp
mean-square of the fluid motion, p and p are the densities of the particle and the fluid respectively, V is the fluid viscosity, and d is the diameter of the particle. This equation is used to show that the pliolite trace particles indeed follow the fluid motion. Johnson notes that cTL is very large even for small values of T . He mentions also that $ is very close
L
to one. Thus, with aTL very large and 8 approximately one, the pliolite particles follow the fluid flow. However, it was found that the actual value of a for pliolite and water at 20�C is 0.98 which shows his use of 0 equal to one is very close. Even if the quantity aT was equal to
L
zero, U' would still be 96% of U' which is still reasonably close to the fluid motion.
3.2 Prism Analysis and Calibration
The two prisms were mounted on the plexiglass test pipe with castor oil filling the gap between the flat face of the prism and the curved pipe wall as shown in Figure 2.2. The intersection of the two smaller faces of the prism was parallel to the longitudinal axis of the test pipe. Castor oil was chosen to fill the gap because its index of refraction (1.48) is very close to the plexiglass (=1.49) and crown glass (1.52). A common index of refraction of 1.50 was chosen for the prism, castor oil, and pipe unit for ease of analysis since very little error was introduced.
Viewing the trace particles in the fluid through the prism yields
two images for each particle as seen in Figure 3.1 from the camera position. The distance between these images is related to the Y coordinate while the difference in positions of these images from the two face intersection is related to the Z coordinate. The X coordinate is measured relative to any fixed reference location along the longitudinal axis of the pipe. The general field of view in the fluid as seen through the prism is sketched in Figure 3.2. This flow field volume cross section is a circle sector with its apex from the pipe wall determined by the prism dimensions as detailed in Chapter II and partly shown in Figure 2.3.
For a prism mounted on the test pipe illustrated in Figures 3.1 and
3.2, the complete derivation of equations for relationship between the image positions and the particle position is developed in Appendix A. The origin of the Cartesian coordinate system is at the center of the pipe (Figures 3.l(A-l)and3.3k-2)). The equations are written for two paths from point A to point P (ABCP and AEDP) by writing the equations of the individual lines and intersecting them as shown in Figures 3.1 and 3.3.
Introduction of the angle allows the derivation to compensate for a misaligned camera. Angles i and j are angles of incidence. Since
the pipe wall is curved, the normal to the pipe wall associated with angle j changes with respect to the Cartesian coordinate system as the image position in the prism moves away from the Y axis (as B or E gets further from the center of the prism).
The results of the derivation in Appendix A are equations which locate the particle position in the pipe based on ZB, ZE, the indices of refraction, and the geometry of the pipe-prism unit. The equations are
ZC Cot(C + Y C) + ZD Cot(D+YD) - R2 Z2 + /R2 -Z2
z C C C C D
P Cot(OC + YC) + Cot(OD + Y(D
(3.1)
Y /R2 - Z2 + (Z - zC) Cot(C + Y (3.2)
p C P ) C t(%
where
0C Tan-1 ZC - Tan1 -ZD
C ( )D anl
D N
CD
Sin[N Sin( 0C - Sin-1[ N Sin( Q)])]
w g
N -1 N
D : Sin-l[ N9 Sin( j - D - Sin-l[ N a Sin( L - Q1))]
w g
-b+k2 - 4ac
Z C =2a
with
a = Tan2(S + 6C) + 1
22
b 2[h -ZB Tan(- )] Tan(Q + ) - 2Z Tan2 ( + 6
B=[- Ta C B C
c [h - ZB Tan(- Q)] 2 R- 2[h -Z Tan( - 1)IZB Tan(Q + 6 )
2 Tan2 (1 + C
B ZB
Z -e -e2 - 4df
2d
with
d = Tan 2(1 + 6 D) + 1
e = 2[h - ZE Tan( - Q)] Tan(2 + 6D) -2ZE Tan2 (Q + 6D)
2 2 D
f= [h - ZE Tan(7- )] - - 2[h - Z Tan( -2)]ZE Tan(2- 6)
E 2E 2E D
+Z2 Tan( + 6D)
E D
N
6 = Sin- [
C N
g
N
6D Sin-l[a
g
Sin( 1-- 1 + )] Sin( - -
These equations are valid for any position of a particle in the
prism field of view. The equations relating the image positions to the flow space particle position were then written into a computer program which was checked for validity by placing a grid with line intersections at known locations in the fluid behind the prism. This validity check
and
was done for both the large and small prism. Each was checked in two ways. In both cases the first way was byamanual graphics method. The second way was by use of the method of data reduction utilized to reduce the data acquired through that prism. The second method for the large prism was done by using the Pictorial Data Acquisition Computer, while the second method for the small prism utilized the data tablet/digitizer. Both second methods will be discussed in detail in Chapter IV. The first method (manual graphics) was the same method used by Johnson, 1974, to check the validity of the equations for the small prism. This method consisted of filming the prism with the grid in the fluid behind the prism, mounting the film in a slide projector, projecting and tracing the grid from the film to graph paper, measuring the positions of the intersections, and processing the data through the prism equations computer program with the appropriate scale factor. The scale factor for the present work was determined for the change in the X coordinate, which was unaffected by the prism, and was checked by relating the graph paper prism size to the actual prism size. Table 3.1 shows the results. The calculated positions agree with known positions although there were some noticeable differences for small values of the Y coordinate (farthest from the prism) and for large absolute values of the Z coordinate (vertical distance from the XY plane). These discrepancies can be attributed to the use of a single index of refraction for the prism-pipe unit and the fact that small errors in reading become slightly larger errors in true position with a decreasing Y coordinate and an increasing Z coordinate.
3.3 Operation of the Experimental System
This section describes the operation of the experimental flow apparatus and the data acquisition equipment as an integrated unit.
The discussion will encompass the general operation of this equipment. It will discuss the start up and running, the data acquisition, and the shutdown. Figure 2.1 shows the experimental flow apparatus and Figure 2.2 shows the data acquisition equipment.
When using the experimental pipe flow apparatus, the fluid level tube on the side of the storage tank (9, Figure 2.1) should be checked before the pump is turned on. This will ensure adequate fluid for operation of the pipe flow apparatus. The proper fluid level is marked on the fluid level tube. The electronic equipment must be warmed up prior to use for 15 to 20 minutes (vacuum tube voltmeter, strip chart recorder, and flowmeter). Both cooling units (cooling elements located in 1 and 8, Figure 2.1), have to be turned on and the desired temperature set on the Blue M unit rheostat. The pump (7, Figure 2.1) is then turned on with both control valves (6, Figure 2.1) closed. When the fluid is seen in the sight glass on the overflow line from the constant-head tank (between I and 8, Figure 2.1), the large line control valve is opened quickly to pick up any pliolite particles that have settled out of the fluid from previous experiments. The valve is then closed and the strip chart recorder and vacuum tube voltmeter are "zeroed". At this point, the temperature of the fluid is noted (4, Figure 2.1) and the flow rate is adjusted for the desired Reynolds number using a graph plotted for this purpose. As precautionary measures during each experimental run, check the strip chart potentimetric recorder for a constant reading, the sight glass for fluid (constant head), and the thermometer for a constant temperature.
Caution in the data acquisition procedure can reduce or eliminate many
problems in the data reduction phase. For maximum light intensity, the projector
light beam must be collimated in such a fashion that at the prism location it illuminates only the convergent flow region viewed through the prism as discussed in Chapter II. If the beam illuminates any volume outside of the flow region to be mapped, particles will be illuminated which can be seen through only one face of this prism. This will produce series of single view positions of particles that cannot be matched to images in the other prism face rendering the matching of image pairs much more difficult. The limited illumination can be accomplished by using a shaped hole in a black slide in the projector. With the proper illumination accomplished, the movie camera is set up. For the small prism, a 152 mm telephoto lens with a close up adaptor, and for the large prism, a 100 mm telephoto lens with a close up adaptor were found to fit adequately the vertical dimension of the prism onto the movie film. For the proper depth of field, an aperture setting of 11 was used for the small prism and an aperture setting of 16 was used for the large prism. The electronic counter was filmed before and after the film record was made in order to check its rate and continuing constancy.
The shut down of the experimental pipe flow apparatus is accomplished by turning off the pump and coolers. This was done without closing any valves before the fluid level tube on the storage tank indicated that the quiescent water level is again attained.
TABLE 3.1 CALIBRATION VALUES FOR PRISM ANALYSIS CHECK
Data for large prism:
True (Z) = 0.00
Calculated (Y)
63.5 63.4 59.9 54.9 49.4 45.1
39.5 34.8
30.0 20.0 15.3 11.1
7.2 0.1
0.0 0.0 0.0
0.0 0.0
0.0
7.05 14.10 21.15 28.20
Calculated (Z)
14.2 14.3
14.1
21.2 21.5
True (Y)
63.5 63.4 60.0 55.0 50.0 45.0 40.0 35.0 30.0 20.0 15.0 10.0
5.0 0.0
28.2
28.6
28.0
Data for small prism:
63.5 60.0
54.8 50.0
44.2 40.0 30.0 25.0 20.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
7.0 7.2 7.1 7.1
7.0
6.9 6.7
14.3 14.0
By tablet:
63.5 59.8 55.0 50.0
45.0 40.0 34.8
29.9 24.6 19.8
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0
0.0
7.0 7.2 7.2 7.1 7.1 7.1 7.0 6.9 7.0
6.8
14.3 14.3 14.2 14.1 14.1 14.1
14.4
21.0
63.5 60.0
55.0 50.0
45.0 40.0 30.0 25.0
20.0
63.5 60.0
55.0 50.0 45.0 40.0
35.0 30.0 25.0
20.0
FIGURE 3.1 Prism, pipe, and camera
Field of view Shell section for velocity averaging -
FIGURE 3.2 Prism arrangement with field of view in flow
FIGURE 3.3
Prism and pipe
CHAPTER IV
METHOD OF DATA REDUCTION
4.0 Introduction
Data reduction begins by translating the cinematographic record of trace particle images to digitized data for the IBM 370 Computer. This has been accomplished using the Pictorial Data Acquisition Computer and the Scriptographics data tablet/digitizer. The output of both of these methods is a set of two dimensional particle image locations as recorded on the film frames. These image locations grouped by frame, served as the input data for a program which followed the images from frame to frame as they traversed the fluid volume visible through the prism, and matched each pair of the two particle image series that corresponded to a particle entrained in the flow. The data were then processed through a program that solved for the three dimensional positions of the particles, filtered out noise associated with the conversion of data from cinematographic records to computer recognizable locations, solved for velocities, and interpreted the data statistically. Part of the output was the positions and velocities of the particles as they moved through the prism visible region. These data arranged by particle path, were used in a program that plotted a three dimensional perspective view of the reconstructed particle paths and in another program that rearranged the data by frame (constant time grouping) for use in a display of instantaneous velocity fields. The input to the velocity field display program was either directly from the rearranged data or the output of a
program that interpreted the velocities at known grid pontro from the rearranged particle position data. The general flowof data through the method of data reduction is flowcharted in Figure 4.1. The number beside each step refers to the corresponding section in Chapter IV.
4.1 Pictorial Data Acquisition Computer Method
The first method of converting cinematographically recorded data to digitized data recognizable by the computer was a method using the Pictorial Data Acquisition Computer (PIDAC) located in the Picture Processing Laboratory at the University of Florida's Center for Information Research. The PIDAC is a flying spot scanner system interfaced with an IBM 7094-II computer. The PIDAC was designed for biomedical research but it possibly seemed to be adaptable for processing trace particle image records into digital information for use in the IBM 370 computer operated by the Northeast Regional Data Center located at the University of Florida.
The flying spot scanner consists of a high intensity light source,
a converted Nikon still camera, and an image scanner. The high intensity light was directed through the lens of the Nikon camera onto the film frame which was placed in the camera. The light that passed through the
2
film was picked up by the image scanner. As it was set up, the 35 x 24 mm still camera slide was scanned in 648 lines along the 35 mm side and 464 lines along the 24 mm side. Since the 35 mm cinematographic camera takes half still camera frame sized frames, two frames could be processed at one time. This meant that the effective scanning of one movie frame was 464 lines by 324 lines. This corresponds to a spatial sampling of approximately 0.05 mm on the film or approximately 0.27 mm on the large prism which was used to acquire data for this method.
DATA ACQUISITION
(Chapter I II )
PICTORIAL DATA AcQUISITION COMPUTER (1)]
I M
I I
PARTICLE IMAGE FOLLOWINGANIMG SERIES MATCHING (3)
i 3-D POSITION AND VELOCITY (4
I
DATA TABLET/ DIGITIZER (2)
T
OUTPUT: average velocities and RMS values
REPUNCH BY FRAME (4)
PARTICLE PATHS (6)1
OUTPUT: 3-D perspective view of particle paths
GRID REFERENC ING (5]1
OUTPUT: grid position and velocities
I VELOCITY FIELD (61
OUTPUT: 3-D perspective velocity fields, 2-D R-e 2-D X-R views
view of views, and
Flowchart of the method of data reduction
FIGURE 4.1
The output of the scanner could be viewed on a storage cathode ray scope before it was processed through the IBM 7094-11 computer and recorded on magnetic tape. This visibility was useful in determining the optimum intensity level of the light source to yield the highest quality particle image output possible. Since the storage scope has a memory, several frames could be displayed simultaneously to ensure that the particle image could be seen from frame to frame as it traversed the viewing area. In this step, an eight level (0-7) light intensity output was associated with each scan intersection.
This was a tremendous amount of information since there were more than 300,000 locations each with eight computer bits of information required for every two cinematographic frames scanned. The data could be reduced by a factor of eight by putting this information in binary form since only one bit would be required for each scanned intersection. This was acceptable because the only information necessary was whether or not a particle image was at the intersection, not its intensity level. This was accomplished by processing the data through a binary conversion program using a threshold intensity level. If the intensity number was at or below the threshold level (6), the number "" would be associated with that location, while above that level the location associated number would be "0". The output of this process was put on computer tape.
The final part of the PIDAC phase of data reduction was to process
the binary data through a computer program that ultimately yielded Cartesian coordinate locations for the center of each particle image. The program encoded the boundary of each particle and solved for its center location in Cartesian coordinates. Two prism fixed reference marks were included on each cinematographic frame. These marks were used in the next section
of the program to orient the images of each frame to an XY coordinate system which was nonvarying with respect to the prism. This was accomplished by designating the left reference mark center as the origin, and rotating all the data around this origin so that the right reference mark center was on the X axis. This operation corrected the data for mispositioned and misaligned film in the camera film mount of the flying spot scanner or a misaligned cinematographic camera. The output, then referenced and rotated, was recorded on computer cards. These computer cards formed one of the input data sets for the program described in the method of following particle images and matching image pairs.
The major advantage of this system is the speed and ease with which the data were processed. The method utilized by Johnson, 1974, required manually mounting the frames in slideholders, projecting the slides, marking the particle image centers, following the images, and matching the image series that corresponded to particles. The automatic scanning process accomplished the first three steps several orders of magnitude faster and with considerable less effort. However, there are two major trouble spots in the PIDAC method which made the method only marginally capable of yielding useful data. The first problem was the scan interval since it could not be altered appreciably. There were 424 by 324 scan positions for each cinematographic frame record corresponding to an interval of 0.05 mm on the film or 0.27 mm in the viewed 113 mm base prism. The particles used were from 48 to 80 pm in size. The cinematographically recorded particle image diameters were three to five times smaller than the scan width. This resulted in the possibility that particle image center locations could be in error by as much as + 0.1 mm in the X and Y locations. It was also possible to miss an image position entirely if
the recorded image was less dense than most of the others. A recorded image could also be lost if it was located near the outer limit of the scan line width since the sensitivity of the scanner is diminished considerably near the line limits. The missing of a particle image would interrupt the image series and cause the loss of much data. The accuracy and data loss problems could be considerably reduced by using a unit with higher resolution. The second problem with the system was that the lensing of the flying spot scanner did not allow uniform illumination of the film. The center of the scanned area received the most illumination with the intensity decreasing radially toward the boundaries. This caused a radial decrease in particle image density with progressive loss of data toward the scan area boundaries. This is a compounding problem since the particles farthest from the prism in the test pipe, which appear smaller and less intense on the cine film, were closest to the upper and lower boundaries of the cinematographic frames and, consequently, the upper and lower boundaries of the scan area.
4.2 Data Tablet/Digitizer Method
The second mode of converting cinematographic records to digitized data recognizable by the IBM 370 computer was to utilize the Scriptographic data tablet/digitizer. The movie film was enlarged using a standard photographic enlarger and projected onto a standard 0.279 by 0.279 m Scriptographic data tablet/digitizer manufactured by Summagraphics. The data tablet was interfaced with the IBM 370 computer through a terminal control program (TCP). The location of each particle image was digitized by touching the data tablet at the center of each projected image with the recording stylus. The coded tablet coordinates of these positions were then transmitted to the computer. The physical principles of the
data tablet's operation are explained in Summagraphics Corporation, 1973, p.2, Response to a questionnaire from the University of California on April 30, 1973,
Magnetostriction and inverse magnetostriction. The substrate under the vinyl surface is a magnetostrictive metal. Currents
are pulsed along the X and Y axis, setting up plane strain waves in the metal. As these waves pass under the small pick-up coil
in the stylus (cursor), the inverse magnetostriction produces an electrical signal. Digital data is derived from counters which begin counting when the 'start' currents are pulsed and end the
counting when the 'stop' signal is received from the stylus (cursor).
The relative coordinates of the image centers were verified by viewing each frame on a Tektronix 4013 cathode ray tube storage scope. The data were next stored on computer discs and computer cards. The last step of this operation was to process the raw output (symbols) through a computer program that converted the symbols to useful coordinate data.
The program took as input the symbols from the data tablet/digitizer and converted them to locations related to test pipe fixed coordinate system so that it would not vary from frame to frame. The input symbols were first processed through the subroutine called "XLT" which translated them to numbers. The first two data points entered were the left and right reference marks from the film. The left mark was used to reference the data to the tablet origin and both marks were used to reference the data to the tablet horizontal. At this point each frame was referenced to the same origin with the same orientation. This operation corrected the data for mispositioned and misaligned film in the enlarger or a nonaxially aligned data acquisition motion picture camera. The data were next recorded on computer cards and became the second input data set for the program described in the method of following particle images and matching image pairs. The complete program is shown in Figure 4.2.
Although this method of converting visual data to digital data was
tedious and time consuming when compared to the PIDAC method, it was still
several orders of magnitude faster than the manual method applied by Johnson, 1974. It did not have the lighting and scan width problems associated with the PIDAC method. The high intensity light from the enlarger made the particle images very easily seen on the tablet surface so data were not lost in the process of digitizing.
The errors in position associated with digitizing data by this
method were the result of the angle of tilt of the stylus from vertical, the accuracy of the tablet, and the human error of location. The error caused by tilting the stylus was a line count shift which was two counts for 220 and four counts for 45'. The shift was in the direction of the tilt only and was a shift not a random error. If, as was the case, reasonable care was taken to ensure that the sylus was held at approximately the same angle, no relative shift would be induced between particle image locations. The absolute shift was compensated for by the fact that the shift was also in the two referencing marks. The manufacturer specifies an accuracy of + 0.127 mm for location specification on the tablet. The data processed with the data tablet/digitizer were obtained using the small prism. The maximum errors in the specification of location in the flow region that can possibly result from the data tablet accuracy are + 0.035 mm in the longitudinal coordinate, + 0.075 mm in the radial coordinate, and + 0.025 mm in the circumferential coordinate. It should be noted that the largest error was in the radial direction as would be expected from observing the image rays in the derivation of the prism equations in Appendix A since small deviations in image position result in large radial and small azimuthal deviations in particle position. The radial root-mean-square velocity i s the primary component used to confirm the maximum frequency retained after noise filtering reported in Chapter V, since it containes the largest maximum error and i s the
38
easiest to distinguish. Taking into account the particle image size as projected on the tablet, the estimated human error in particle center location was less than one-third of the radius of a particle or + 0.01 mm in true position in the test pipe. Both m a c h in e and human errors could be reduced to less than one-third by using the now available 0.914 by 1.219 m tablet and enlarging the frame to fit the larger tablet which has the same + 0.127 mm resolution associated with it.
651-FOLLCW -FORT -SYSPRINT
LEVEL 2.1 ( JAN 75 ) 05/360 FORTRAN H EXIENDED DATE 76.239/20.
REQUESTED OPTIONS: NC0ECK9NOLCAADsCPT=0
OPTIONS IN EFFECT: NAVE(MAIN) NOOPTIMIZE LINECOUNT(74) SIZE(CAX) ALTOCEL(NCKE) SOURCE ESCDIC NOLIST NODECK NOOBJECT MAP NOFORMAT GCSTMT NCXREF ALC NOANSF NOTER
C THIS PROGRAM ANC THE DATA INPUT METHOD WAS DEVELCFEC EY
C GARY JACKMAN AND RANDY CROWE
C THE INPLT IS BY MEAIS CF A X-Y TABLET
C TI-E PROGRAM USES REFERENCE MARKS CS% THE FILM 7C RCTATE ALL FRAMES
C TC TABLET HORIZONTAL AND TRANSLATE ALL FRAME BOUNDARIES TO THE
C SAME X-Y COORDINATES
ISN 0002 INTEGER CATA(50C,4),XTvYTXS(500),YS(500)
ISN C003 INTEGER X IYIX2,Y2,XYD(4)
ISN 0004 LOGICAL PNCH
ISN 0005 REAL*4 NAME(5)
ISN C006 DATA STOP/vSTOP"/
ISN 0007 READ(51001) XT,YT
ISN 0008 1001 FORMAT(214)
ISN 0009 READ (591002) PNCH
ISN 0010 1002 FORMAT(LI)
ISN Col I READ(5,1003) NPTSNAME
ISN 0012 100- FORMAT(14,5A4)
ISN 0013 [F(NPTS*EG*O) GO TO 5C
ISN C015 IF (NAME(I).EC.STOP) GC TC 50
ISN 0017 READ(5,1000) ((DATA(I.J).J=1,4),I=1,NPTS)
ISN C018 IC CONTINUE
ISN C019 11 CONTINUE
ISN 0020 WRITE(6,1010) ((DATA(I.J),J=1,4),I=INFTS)
ISN 0021 101C FORMAT('1 ,//,10X,'RAW DATA',/(* -",120(4AI),'-*,/))
ISN 0022 100C FORMAT(20(4A1))
ISN 0023 00 21 J=1,4
ISN 0024 21 D(J)=DATA(IJ)
C XLT(DXY) DECODES Tf4E TABLET SYMBOLS TO X-Y COORDINATES
ISN C025 CALL XLT(D*XY)
ISN 0025 X1=)
ISN C027 YI=Y
ISN C028 ARITE(6,9100) X1,YI
ISN 0029 10C FORMAT(///1 OXv$POINT 1: '92110)
ISN C030 920C FORMAT(IOX,'PCINT 2: ',2110)
ISN 0031 O0 22 J=1,4
ISN 0C32 22 C(J)=DATA(2,J)
ISN CC33 CALL XLT(DXY)
ISN 0034 X2=X
!SN C035 Y?=Y
ISN C036 ARITE(6,'920) X2,Y2
ISN C037 ANG=FLOAT(Y2-YI)/FLOAT(X2-X1)
.FIGURE 4.2 Computer program for converting data tablet coded coordinates to referenced X-Y coordinates
ISN 0038 ANG=ATAN(ANG)
ISN 0039 %RITE(6,9000) ANG
ISN 0040 90CC FORMAT{IOX,'ANGLE: ",FIO.4)
ISN 0041 C=CCS (ANG)
ISN C042 S=SIN(ANG)
ISN 0043 CC 20 1=3,NPTS
ISN 0044 Do 25 J1l,4
ISN 0045 25 D(J)=DATA(IJ)
ISN 0046 CALL XLT(DXY)
C THIS SECTION RCTATES AND TRANSLATES THE DATA ISN 0C47 XS(I-2)=-U(C*(X-Xl)+S*(Y-Y))-XT)
ISN 0048 YS(I-2)=((-S*(X-XI))+C*(Y-Y1))+YT
ISN C049 2C CONTINUE
ISN 0050 NPTS=NPTS-2
ISN 0051 %RITE{6,1100) NAME.NPTS,((XSI),YSCI)J,1=INPTS)
ISN 0052 1100 FORMAT ('l',//,IOX,'FRAME ID = *,5A49/,
.IOX.'NUM-BER CF PARTICLES = '*144
./I, ' " 9(21591 ' ),/))
ISN 0053 WRITE(7, 1201) NPTS,NAME
ISN 0054 1201 FORVAT(I4v5A4)
ISN 0055 WRITE(7,12CC) ((XS(I).YS(I)),I=1,NPTS)
ISN 0056 1200 FORMAT(10(214))
ISN 0057 4C CONTINUE
ISN 0058 GO TO I
ISN C059 50 CONTINUE
ISN 0060 STOP
C
FIGURE 4.2 - continued
R-CUESTED OPTIONS: NCCECK,NCLCAD,CPT=O
OPTIONS IN EFFECT: NAtE(MAIS) NOOPTINIIZE LINECOUNT(74) SIZE(MAX) ALTODELNCKE) SCURCE EBCDIC NOLIST NODECK NOOBJECT MAP NOFORIAT GCSTMT NCXREF ALC NCANSF NOTER
ISN 0012 SUBROUTINE XLI(DATA,XY)
ISN 0003 INTEGER DATA(4),CHR(32),XY
ISN 0004 DIMENSION ND(4)
ISN CCO5 DATA CHR/9 ", 9 ,9 0 I , I$ " " I% 5 " )I 1 0* 2.0+9 it "
ISN 0006 DO 2 J=1,4
ISN 0007 DO 1 1=1,32
ISN 0008 IF (CHR(I).EQ.DATA(J)) GO TO 2
ISN 0010 1 CONTINUE
ISN Coll 2 NO(J)=I-1
ISN 0012 X=ND(3)*32+ND(4)
ISN 0013 YND(1 )*32 ND (2)
ISN 0014 RETURN
ISN 0015 END
FIGURE 4.2 - continued
OS/360 FORTRAN H EXTENDEC
LEVEL 2.1 ( JAN 75 )
DATE 76,239/209,
4.3 Method of Following Particle Images and Matching Image Pairs
As discussed earlier, the particle position in the'test pipe is related to-the positions of the two particle images as viewed in pairs through the faces of the prism. One image is on the upper face and the other image is on the lower face. Each frame of the cinematographic record specifies the relative positions of all images of particles within the test volume of the pipe flow viewed through the prism at a given instant in time. Identifing each particle image and recording its position from frame to frame as it traverses the viewed flow field behind the prism is the first step towards a numerical reconstruction of the particle path in the test volume. The next step is to pair the series of particle image positions in the lower prism face with the series of positions of the particle image in the upper prism face that correspond to the same individual particles in the fluid. The prism equations relate the image positions to the position of the particles in the pipe test volume. The data needed to accomplish the following of the image from frame to frame and matching image pairs are the particle image positions from the PIDAC or the Scriptographic data tablet records.
The algorithm for this program imitates the procedure of a human operator in following the images and matching related pairs. This is a first generation program so it necessarily imitates only the simplest human procedures. In succeeding generations, it should be possible to develop more sophisticated programs. As it stands now, the program follows the position of the image from frame to frame by using the preceding two positions to construct a vector to the expected next position. It then uses a tolerance in both the X and Y coordinates to allow for deviations from the expected positions. This is done repeatedly until the image is no longer visible in the prism. The human eye uses this
procedure to follow a moving object. This method is quite successful if the images are sparse enough and the image paths cross each other infrequently. The start up of a series is more difficult since there is no reference for displacements between frames. This is compensated for by choosing a distance that the image could not have exceeded between frames, using the vector construction procedure described above on each image in this area and finding the second frame image that has a third frame image within the specified tolerance in X and Y. Next the program scans the image series in the upper prism face for that series which corresponds to the same particle. This is easy to do since it only entails comparing the X coordinates of the series in the same frame over a sufficient number of frames to be sure that they are traveling identically in X.
It is possible that if two series should cross, the computer
following series would jump from one particle image series to the other. If two series or image paths were to come close enough to each other, it would also be possible to have a series jump. This would result in losing both series and their matches in the other prism face, or, in other words, losing two particle paths in the fluid. The higher the particle density, the more likely it is that this will happen. The human operator solves this problem by following the series as far as possible, skips the doubtful section, and constructs new series after the doubtful area. Next, he constructs the series from the other prism face record and matches it to the original image path fragments to sort out the confusion. The second generation program should use a similar procedure. While the computer matches image pairs it also follows the series using a trace back method to resolve cross-over problems. This program should thus be able to handle seven or eight times the data of
the present program. The approximate amount of particle images that can be handled by this method is at present 150 to 200 which corresponds to 75 to 100 particles in the flow region at any one time. As we will see later, four or five times this much data are the minimum amount necessary to give a good description of the instantaneous characteristics of the flow regions used in these experiments.
Since the program is lengthy and several modifications may be
necessary, the program and modifications are discussed in a brief verbal flow chart below. The complete program is listed in Figure 4.4. All references to the program are in sequential order. The first section of the program follows the image centers from frame to frame as they traverse the flow field. The first part of the first section identifies an image and starts the tracking process. The second part tracks the image until it disappears. The second section pairs the two image series that are associated with the same particle.
In order to follow a particle image, it must first be identified. The method of identification or start up for a particle image series consists of choosing an image position in the first frame in which it appears and constructing a digital window through the X coordinate of the first frame image position and the maximum distance the image could be expected to travel in + X and + Y. This is referred to as "WINDOW 1" in the program in Figure 4.4. All images in the second frame that appear in this window are identified as possible second frame positions for the series. Vectors are calculated between the first frame image and each of the second frame images. The vectors are then extended from the second frame positions with the same magnitude and direction. A second window, "WINDOW 2" in Figure 4.4, is constructed around the end
point of each vector extension. Figure 4.3 shows an example of the windows and particle image positions. The data from the third frame are searched for an image position in any "WINDOW 2". If no image position is found in any of the second windows ("WINDOW 2"), the image position of the first frame is considered noise and discarded. If one image is found in a second window, the image position in the first frame is considered the start of a series, and the image positions in frames two and three that were located in successive windows are added to the series and removed from the data. If more than one image position is found in the second window, the first one tested by the computer will be chosen. If more than one image position is located in the second window, there is a high likelihood of error. The computer print-out will indicated how often two or more images were found in the second window and which frames. If this happens too many times, the size of "WINDOW 2" must be decreased. The window sizes must be changed by the program user to reflect the changes in flow conditions. The higher the flow velocity the larger the window widths but the smaller the window heights required. "WINDOW 1" is varied by changing "WIDTH 1" and "HEIGHT i", and "WINDOW 2" is varied by changing "WIDTH 2" and "HEIGHT 2". Figure
4.3 illustrates the start up procedure. The computer tracks the particle image through the flow field by constructing a vector from the last position by an equal magnitude. "WINDOW 2" is digitally constructed around this expected location. The data of the next frame aresearched for an image position in this area. The image position identified is added to the series and removed from the data. If no image position is located in the window, the series is terminated. When all the image positions of a frame have been added to the proper series and removed from the data, the remaining image positions are treated as first
positions for start up as previously described.
After the particle image series are constructed, they must be paired to completely define each particle path in the flow field. This is accomplished in the last section of the program which is labeled, "Try to match a pair of identified series". The series in the lower prism face are taken one at a time and tested against each series in the upper prism face. In virtually all cases, the initial frame number of each two series that successfully paired were within two of each other. Consequently, this was checked first to eliminate series from the upper prism face that could not be matched, thus saving much computer time. The X coordinates were compared until a series in the upper prism face coincided with the series in the lower prism face being tested 15 times. This was considered to be a sufficient number of matches to determine the image pairs of a particle. The errors discussed earlier made it necessary to put a tolerance on the X coordinates of the upper prism face series. The tolerance used in this case was six data tablet units which was much larger than the errors but small enough not to cause pairing mistakes.
Employment of this program may necessitate change in various parts
for compatibility with the data. In the section concerned with following images, it may be requisite to change the window sizes, the maximum length of the series, the maximum number of series, and the number of frames of data to be considered. In that section of program pertaining to image series matching, it may be essential to alter the number of matches to consider two series paired, and to change the tolerance on the X coordinates of the upper prism face series.
The output from this method is the paired series that define the
particle paths in the flow field. The information for each series pair is the particle number, the initial frame number, and the list of image positions by frame on computer cards. This information is the input data necessary for the method for determination of three dimensional positions and velocities. The printed output is the image series from the first section of the program and the paired series output with both of the X and Y values from the second section. This permits a manual check of paired series for accuracy and makes it possible to manually match more series if necessary.
Wi ndow2
-----I
I I
I I
I I
I I
I I
Wi ndowl
* Particle position in frame I Particle position in frame 2 0 Particle position in frame 3 Wi ndow2
I I"
Wi ndow2
I I
FIGURE 4.3 The particle image series startup process
230-FOLLOW -FORT -SYSPRINT
LEVEL 2.1 ( JAN 75 )
0S/360 FORTRAN H EXTENDED
DATE 76.251/15
REQUESTED OPTIONS: NODECK.NOLOADOPT=0,LC(48) OPTIONS IN EFFECT: NAME(MAIN) NOOPTIMIZE LINECOUNT(48) SIZE(MAX) AUTODBL(NONE) SOURCE EBCDIC NOLIST NODECK NOOBJECT MAP 4OFORMAT GOSTMT NOXREF ALC NOANSF NOTER
ISN 0002
ISN 0003
ISN 0004 ISN 0005 ISN 0006 ISN 0007 ISN 0008 ISN 0009
ISN 0010
ISN 0011 ISN 0012 ISN 0013 ISN 0014
ISN 0015 ISN 0016 ISN 0017 ISN 0018 ISN 0019
INTEGER WINDY1,WINDY2.WINDX1,WINDX2,WIDTHIWIDTH2,HI.GHTI,HIGHT2,
I DELTA X, DELTA, COUNT
INTEGER IMAGEI(2).WINDXWINDY,IMAGE2(2).SERIES( 800,63) ,FRAME(
13,400),NP(,3),FLAG(3,400),FLAG2,FLAG3SIMAGE3(2) .FLAG!
C ORIGINAL FLOW CHART BY OR R E ELKINS C ANALYSIS FOR APPLICATION BY GARY R JACKMAN C PARTICLE FOLLOWING PROGRAMED BY DR J K YOO C SERIES MATCHUP PROGRAM BY GARY R JACKMAN C PARTICLE IMAGE IDENTIFICATION PROGRAM C THIS PROGRAM FIRST IDENTIFIES A SERIES OF A PARTICLE IMAGES C THEN MATCHES PAIRS OF SERIES THAT DEFINE A PARTICLES MOTION
C PARTICLE IDENTIFIER C FLAGS =0:NOT TESTED OR NOT IC=ENTIFIED C FLAGS =I:TESTE'm IN FRAME AND IDENTIFICATION IN PROGRESS(FRAME 2,3) C FLAGS =2:SELECTED AS A SERIES OF A FLOW IMAGE C FLAGS =3:TESTED AND CONSIDERED AS NOISE C SERIES(I):PARTICLE ID C SERIES(2): INITIAL FRAME C SERIES(3): NO* OF PARTICLE IDENTIFIED IN SERIES C INITALIZATION OF FLAGS AND SERIES
DO 1000 KOOK=I,400
DO 1000 JAE=I,3 1000 FLAG( JAEKOOKJ=O DO 1001 KOOK=I,63
DC 1001 JAE=I, 800 1001 SERIES(JAEKOOK)=O C SET INITIAL FRAME NUMBER=1
I FRAME=1
C DEFINE WINDOW SIZES
WIDTH1=30 HIGHT1=16 W I DTH2=20 HIGHT2=16
C READ THREE FRAMES FROM CARDS, WITH FRAME=J
COUNT= 1
DO 10 J=1,3
READ(5.2001) NP(J) 2001 FORMAT( 14)
NPTWO=NP (J )*2
FIGURE 4.4 Computer program for following image positions and matching image pairs
MAIN OS/360 FORTRAN H EXTENDED
ISN 0020 READ(5200"2) (FRAME(JK).K1lNPTWO)
ISN 0021 2002 FORMAT(2014)
ISN 0022 10 CONTINUE
C REINITIATE FRAME# ISN 0023 101 NPI=NP(1J
ISN 0024 NP2=NP(2)
ISN 0025 NP3=NP(3)
ISN 0026 9 FLAGI=O
ISN 0027 J=l
C SELECT AN UNIDENTIFIED IMAGE FROM FRAME(l) TO BE SET AS AN IMAGEl ISN 0028 2 DO 20 Lt=1.*NP-1
ISN 0029 JLI=LI*2-1
ISN 0030 IF(=LAG(JiL).EE.0) GO TO 1
ISN 0032 20 CONTINUE
C IF ALL THE PARTICLES IN FRAME 1 ARE CHECKED, GO TO 4 ISN 0033 21 IF(=LAG1.EQ*O) GO TO 4
ISN 0035 STOP
C AN UNIDENTIFIED PARTICLE IS FOUND, RECORD IT AS IAAGE1 ISN 0036 1 =LASI=1
ISN 0037 FLAG(JL1)=1
ISN 0038 SERIES(COWNT,1)=COUNT
ISN 0039 IMAGEI(I).FRAME(JJL1)
ISN 0040 LLI=L1*2
ISN 0041 IMAGEI(2)=FRAME(J,LL1)
C SET WINDOW AREA
ISN 0042 11 WIN)X=IMAGE1(I)+WIDTHI
ISN 0043 WINDYI=IMAGE 1(2)+HIGHTI/2
ISN 0044 WINDY2= IMA GEl (2)-HIGHTI/2
ISN 0045 111 FLAG2=O
ISN 0046 J=2
C ANY IMAGE IN FRAME(2) IN WINDOW AREA OF IMAGES ISN 0047 DO 30 L2=1,NP2
ISN 0048 JL2=L2*2-1
ISN 004g IF(FLAG(JL2S.NE0) GO TO 30
ISN 0051 LL2=L2*2
ISN 0052 IF(FRAME(JJL2),GEIMAGEI(1).ANDFRAME(JJL2).L.---WINDX.AND.FRAME(J
1.LL2).GE.WINDY2.AND.FRAME(J.LL2).LE.WINDYI) G3 TO 31 ISN 0054 30 CONTINUE
C IF NO PARTICLE- IN WINDOWI.SET IMAGES AS NOISE AND FIND ANOTHER PARTICLE IN
C FRAME(1
ISN 0055 32 IF(FLAG2,NE*O) STOP
C NO PARTICLE IN WINDOW ISN 0057 FLAG( I *L1 ) =3
C RESET FLAGS FDR THE UNACCEPTED PARTICLES IN FRAME2 WINDOW n ISN 0058 DO 321 K=1,NP2
ISN 0059 321 IF(FLAG(2,K)aEQ*I) FLAG(29KJ=o
FIGURE 4.4 - continued
LEVEL 2.1 JAN 75 )
DATE 76*251/15,
MAIN OS/360 FORTRAN H EXTENDED
ISN 0061
[SN 0062 ISN 0063 ISN 0064 ISN 0065
ISN 0066 ISN 0067 ISN 0068 ISN 0069
ISN .0070 ISN 0071 ISN 0072 ISN 0073
ISN 0074 ISN 0075 [SN 0076 ISN 0078 ISN 0079
ISN 0081
ISN 0082 ISN 0083
ISN 0085 ISN 0086 ISN 0087
ISN 0088
ISN 0089 ISN 0090 ISN 0091 ISN 0092 ISN 0093 ISN 0094 ISN 0095
GO TO 9
C YES, THERE FOUND A PARTICLE IN WINDOWl', RECORD IT AS IMAGE2 31 FLAG2=1
FLAG(J-PL2) =1
IMAGE2( 1)-FRAME(J9JL2) IMAGE2(2)=FRAME( JLL2)
C EXTRAPOLATE THE THIRD POSITION BY VECTOR MANIPULATION C FROM IMAGES TB IMAGE2 INSIDE THE THIRD FRAME WINDOW2 AREA
C
C CALCULATE VECTOR
33 DELTAX=IMAGE2(1)-IMAGE1(1) DELTAY= IMA GE2(2)-I.4AGE1 (2)
J=3
C SET WINDOW2 AREA
WINDXI IMAGF2(:I )+DELTAX-WIDTH2/2 WIN:)X2= IMAGE2( 1)+DELTAX+WIDTH2/2 WIN)YI=IMAGE2(2)+ DOLTAY-HIGHT2/2
WI N)Y2=IMAGE2( 2)+DELTAY+HIGHT2/2 C SEARCH FOR A POINT IN THE THIRD FRAME
DO 40 L3=I NP3
JL3=L3*2-1
IF(FLAG(J-*L3),NEs0 GO TO 40
LL3=L3 *2
IF(FRAME(JJL3),GE.WINDX1,AND.FRAME(JJL3),LE.WINDX2,AND.FRAME(J,
ILL3).eGE.WINDY1.AND.FRAME(J,LL3).LEWINDY2) GO TO 41
GO TO 40
C YES. THERE IS A PARTICLE IN WINDOW2 41 FLAG3=FLAG3+1 IF('LAG3GE.2) GO TO 44
C ASSUME THIS PARTICLE IS A PART OF A SERIES CURRENTLY SEARCHING
FLAG( J 9L3) =1
IMAGE3(1 )=FRAME(J*.JL3) IMAGE3(2 )=FRAMEfJ, LL3)
C STORE INITIAL FRAME NUMBER AND NJMBER OF PARTICLES IDENTIFIED IN THIS C SERIES AND IMAGES 42 SERIES(COUNT,2)=IFRAME C STORE SERIES OF THREE IMAGES IN ARRAY SERIES(800,63)
SERI ES (COUNT 3 SERIESEI COUNT, 3) +3
SERIES(COUNT,4=IMAGEI(1) SERI ES(COUNT,5)=IMAGEl(2) SERIES (COUNT 96 )= IMAGE2( 1) SERIES (COUNT ,7 IMAGEG2 (2)
SERIES( COUNT, 8) =IMAGE3( 1) SERIES (COUNT , 9)= IMAGE3 (2)
C SET FLAGS FOR THE IDENTIFIED SERIES
FIGURE 4.4 - continued
.LEVEL 2,1 ( JAN 75 )
DATE 76*251/15*
MAIN OS/360 FORTRAN H EXTENDED
ISN 0096 ISN 0097 ISN 0098 I SN 0099
ISN
ISN
ISN
ISN ISN
ISN ISN ISN ISN
ISN
ISN ISN
ISN ISN
ISN ISN
ISN
ISN
ISN
ISN ISN
ISN ISN
ISN
ISN ISN
ISN
ISN
ISN
ISN
0100
0102 0104
0105 0106
0107 0108
0110 0111
0113
0114 0115 0116 0117
0118 0119
0120 0121 0122 0123
0124
0125
0126
0127
0128 0129
0130 0131
0132
0133
FLAG(3,L3=2
FLAG(2 ,L2)=2 FLAG( l. 1)-2 40 CONTINUE C IF THERE WAS NO MATCH IN FRAME3, GO TO FRAME2TO FIND ANOTHER C PARTICLE IN WINDOW
IF( LAG3,EQO0) GO TO 11
C IF THERE IS AN EXACTLY' ONE PARTICLE IN WINDOW2, THAT IS A SERIES
IF(FLAG3,EQ.1) GO TO 422
STOP
C IF MORE THAN I IN WINDOW2, SET IST ONE AS SERIES AND WRITE MESSAGE 44 WRITE(6v441) IMAGE1 441 FCRMAT('**** MORE THAN 1 PARTICLE IN WINDOW 2 *** FOR IMAGE 2(',21 I5,') ')
C RESET FLAGS FOR THE UNACCEPTED PARTICLES IN FRAME2 WINDOW 422 DO 421 K=I4NP2 421 IF(FLAG(2,KJ.EQ.lJ FLAG(2,K)=O C INCREASE PARTICLE IDENTIFICATION # , IE PARTICLE NAME(COUNT).
COUNT=COUNT+ I
IF(COUNT.oEe 800) GO TO 10C3
C GO TO FIND ANOTHER PARTICLE IN FRAME I
GO TO 9
C ADJUST FRAMES 2 AND 3 INTO 1 AND 2
4 NPNP=NP2*2 NP( I )=NP2
COUNT=COUNT- 1
DO 50 K=INPNP
FRAME( 1,K)=FRAME(2,K) 50 FLAG(1.K)=FLAG(2,vA) NPNP=NP3 *2
NP(2)=NP3
DO 51 K=I-NPNP
FRAME( 2, K.)=FRAME (3, K) 51 FLAG(2.K=FLAG(3*K) DO 52 K=1,400 52 FLAG(39K)=O C NOW READ NEW FRAME3
READ(5,2001) NP(3)
NPTWO=NP(3)*2
READ(5e2002) (FRAME(3,K),K=1,NPT#O) C INCREASE INITIAL FRAME NO.
IFRAME= IFRAME+1 IFRAM=IFRAME*2
WRITE(6,59.) IFRAM
59 FCR?4AT(sFR.AMEf.i5, 8 IS ENTERED#). C NUMBER OF FRAMES TO BE WORKED
FIGURE 4.4 - continued
LEVEL 291 ( JAN 75 )
DATE 76.251/15*
MAIN OS/360 FORTRAN H EXTENDED
ISN 0134 IF(IFRAM.E.168) GO TO 1003
C EXTRAPOLATE A POINT BY VECTOR FROM THE LAST TWO POINTS.
ISN 0136 DO 60 K=.COUNT
ISN 0137 IF((IFRAM-(SERIES(ri ,3)SERIES(K.2))).GEol1 GO TO 60
ISN 0139 IF(SERIES(K,3JGE,30) GO TO 60
ISN 0141 M8SERIES(K, 3*2+2
ISN 0142 Mg=MS +
I SN 0143 M7=M8-1
ISN 0144 M6=MS-2
ISN 0145 K8=M8
ISN 0146 K9=M9
ISN 0147 DELTAX=SERIES(.KMS)-SERIES(K.M63
ISN 0148 DELTAY=SER.IES(KoMg)-SER IES(K*M7)
ISN 0149 WINDXI=SEr;IES(K,MB)+DELTAX-WIDTH2/2
ISN 0150 WINDX2=SEPIES(KM8)+D-LTAX+WIDTH2/2
ISN 0151 WIN)Y1=SER;IES(IKM )+DELTAY-HIGHT2/2
ISN 0152 WINDY2=SERIES(K,Mg)+DELTAY+HIGHT2/2
ISN 0153 FLAG3=O
ISN 0154 NP3=NP(3)
ISN 0155 DO 61 L3=1,NP3
ISN 0156 JL3=L3*2-1,
ISN 0157 IF(=LAG(3,L3J-NE0) GO TO 61
ISN 0159 LL3=L3*2
ISN 0160 I F (RA ME (3 9 JL3 ).GE. WI NDX 1 .AND FRAME( 3 JL3 )LEaW INDX2 AND.FRAME( 3
1LL3JGE.W1NDYl.AND.FRAM4E(3,LL3)}LE.W[NDY2) GO TO 62 ISN 0162 GO TO 61
C YES, A -ARTICLE IN WINDOW 2
ISN 0163 62 FLAG3=FLAG3+1
ISN 0164 IF( LAG3,GE.2) GO TO 63
C ASSUME THIS PARTICLE IS A PART OF SERIES
ISN 0166 fLAG( 3,L3)=1
ISN 0167 M9=M9+2
ISN 0168 MB=M8+2
ISN 0169 IMAGE3(I)JFRAME(3vJL3)
ISN 0170 IMAGE3(2)=FRANIE(3#LLJ)
ISN 0171 64 SERIES(KM8)=IMAGE3(1)
ISN 0172 SERIES(K#M9)=IMAGE3(2)
ISN 0173 SERIES(K93 )=SERIES(K,3B1
ISN 0174 FLAG(39L3) =2
ISN 0175 61 CONTINUE
ISN 0176 IF(FLAG3,LEI) GO TO 60
ISN 0178 STOP
ISN 0179 63 WRITE(6,44l) SERIES(KvK8),SERIES(KKg)
ISN 0180 60 CONTINUE
C NOW TAKE CARE OF PARTICLES NEWLY APPEARED IN FRAME 1 AT THIS TIME
ISN 0181 C OUNT=COUNT+ 1
FIGURE 4.4 - continued
LEVEL 2,1" ( JAN 75 )
DATE 76=251/15*
MAIN 0S/360 FORTRAN H EXTENDED
ISN 0182 IF(COUNT.GE. 800) GO TO 1003
ISN 0184 GO TO 9
ISN 0185 1003 CONTINUE
C PRINT TEST OUTPUT
ISN 0186 WRITE(6,1006)
ISN 0187 1006 FORMAT('THE FOLLOWING SERIES ARE FOUND' )
ISN 0188 DO 1005 J;1,COUNT
ISN 0189 ITOTAL=SERIIS(.J, 3)*2+3
ISN 0190 1005 WRITE(6.1004) (SERIES(JK),K=,ITOTAL)ISN 0191 1004 FORMAT(/,316,/,10('(',215,'Je))
C TRY TO MATCH A PAIR OF IDENTIFIED SERIES
ISN 0192 JJJ=C
ISN 0193 DO 700 M=1,COUNT
ISN 0194 ISM3=SERI--S(M,3)
ISN 0195 JFRAME=SRFIES(.M.2)"
ISN 0196 IF(ISM3.LT.5) GO TO 700
ISN 0198 IF(SERIES(fM,5).GT.500) GO TO 700
C TRY TO COMPAREt TWO SERIES MN
ISN 0200 DO 70 N= 1,COUNT
ISN 0201 IFM.EQ.N) GO TO 70
ISN 0203 ISN3=SERIES(N.3)
ISN 0204 IF(ISN3.LT.5) GO TO 70
ISN 0206 IF(SERIES4N.5).LT.500) GO TO 70
ISN 0208 IFRAME=SERIES(N,2)
ISN 0209 IF(JFRAMEbGE.IFRAME) GO TO 722
C INITIAL FRAME NO. IFRAME OF SECOND S-RIES IS LARGER THAN JFRAME OF FIRSTSERIES
ISN 0211 IF((IFRAME.-JFRAME).GTo2) GO TO 70
ISN 0213 JK=l
ISN 0214 MK=IFRAME-JFRAME+I
ISN 0215 JAC-= JK-1
ISN 0216 MEET=O
ISN 0217 MDE=ISM3
ISN 0218 MKL=MDEF-MK 1
ISN 0219 NASC=ISN3-MK+1
ISN 0220 IF(NASC.LT.MKL) MDEF=MK+NABC-1
ISN 0222 DO 18 MAN:FMKMDEF
ISN 0223 MX=(MAN+I)*2
[SN 0224 JACK=JACKl
ISN 0225 JX=(sJACK+I)*2
ISN 0226 KFRAM =IFRZAME
ISN 0227 IF(IABS(SE'RIES(M*MX)-SERIES(NtJX)).LE.6) GO TO 17
ISN 0229 GO TO 70
C FOUND ONE MATCH
ISN 0230 17 MEET=MEET+ I
FIGURE 4.4 - continued
LEVEL.2*1 ( JAN 75 )
DATE 76.2-51/1.5
MAIN OS/360 FORTRAN H EXTENDED
ISN 0231 ISN 0233 ISN 0234
ISN 0235 ISN 0237 ISN 0238 ISN 0239
ISN 0240 ISN 0241 ISN 0242 ISN 0243 ISN 0244 ISN 0246 ISN 0247 ISN 0248 ISN 0249 ISN 0250 ISN 0251 ISN 0253
ISN 0254 ISN 0255 ISN 0257 ISN 0258
ISN 0259
ISN 0260
ISN 0261 ISN 0262 ISN 0263 ISN 0264 ISN 0265 ISN 0266 ISN 0267 ISN 0268 ISN 0269 ISN 0270 ISN 0271 ISN 0272 ISN 0273
ISN 0274
IF(MEETGE*15) GO TO 71 18 CONTINUE
GO TO 70
C INITIAL FRAME NO, OF 2ND SERIES (IFRAME) IS LESS THAN OR EQUAL TO C JFRAME OF FIRST SERIES 722 IF((JFRAME-IFRAME)*GT,2) GO TO 70
MK=I
JK=JFRAME--I RAME+1 726 JACK=JK-1 MEET=O
MDEF =ISM3
MKL=MDEF-MK+1
NABC=I SN3- JK+l
IF(NABC*LT .MKL) MDE.F=MK+NABC-1
DO 723 MAN=MK,MDEF
MX=(MAN+1 ) *2
JACK=JACK+1
JX= JACK+I )*2
KFRAME=JFR.AME
IF(IABS(SERIES(MMX)-SERIES(NJX)).LE.6) GO TO 725
GO TO 70
C FOUND ONE MATCH 725 MEET=MEET+.1 IF(MEET.GE.15) GO TO 71 723 CONTINUE GO TO 70
C FOUND A PAIR OF SERIES M,N 71 WRITE(6,711) SERIES(M,1),SERIES(N91) 711 FORMAT(0 SERIES 0,14, ' AND *I4, ARE A PAIR') C (PARTICLE ID* INITIAL FRAME), ((XY.,Z), (X*YZ), ,(OOO). C PUNCH OUT THE OUTPUT IN POSITION INPUT FORMAT
JJJ=JJ J+l
WRITE(6,72) JJJKFRAME 72 FORMAT(215) WRITE(7,75) JJJ.KFRAME 75 FORWAT(I4,2XI4)
DO 73 LNG MKMDEF
LONG=( LNG+,I ) *2
LONG I=LONG+ 1
MALL=( JK+1 )*2+1
MALL I=MALL- 1
JK=JK+ 1
WRITE(7,76) SERIES(MLONG) ,SERIES(N.MA-.L),SERIES(MLONG1) 76 FORMAT( 14,13I3,2X) 73 WRITE(6,731) SERIES(M ,LONG),SERIES(M ,LONGI),SERIES(N ,MALL)
1,SERIES(N MALLL)
FIGURE 4.4 - continued
DATE 76,251/154
LEVEL 2-l' ( JAN 75 )
ISN 0275 731 FORMAT(1X,315,17)
ISN 0276 WR ITE(7.77 )
ISN 0277 77 FORMAT(14H00000000C00000)
ISN 0278 GO TO 700
ISN 0279 70 CONTINUE
ISN 0280 700 CONTINUE
ISN 0281 701 STOP
ISN 0282 EN)
FIGURE 4.4 - continued
MAIN 0S/360 FORTRAN H EXTENDED
DATE 76*25 1/15,
LEVEL 2*1 ( JAN 75 )
4.4 Method for Determination of Three Dimensional Positions and Velocities
The records from the method of following particle images and matching image pairs contain the particle number, the initial frame number, and the listing of coordinates for each image pair of the series for each particle. This information is reduced to three dimensional coordinate series or reconstructed particle paths. The data must be filtered to remove digital noise obscuring the true image positions. The filtered position data are used to calculate the velocity components at each data point and the statistical quantities for the flow field. The results of this method can be used to describe the instantaneous flow field as well as the time and space averaged flow field. This method and its computer program will be discussed in four sections. The first subject addressed will be the conversion of the input series pairs to three dimensional coordinates. The second topic will be the digital filtering out of noise induced by the digitization process. The calculation of instantaneous particle velocities at the particle path data points will be the third area of study. The final subject will be the method of acquiring statistical information about the flow field.
The first step of this method is converting image pairs to three dimensional cylindrical coordinates. The input data are of the form of a series of pairs of two dimensional particle image coordinates referenced to the prism. These pairs consists of three coordinate values: The distance of the image pair along the horizontal from the prism edge, labeled "IX" in Figure 4.5; the vertical distance of the image in the upper prism face from the prism axis (two face intersection), labeled "IZB" in Figure 4.5; and the vertical distance of the image in the lower prism face from the same prism axis (two face intersection), labeled
"IZE" in Figure 4.5. The integers are converted to real numbers and referenced to the p ri sm axis for use in the computer program. These values are processed through the prism equations (3.1) and (3.2) to yield Cartesian coordinates which are converted into cylindrical coordinates for use in the remaining parts of the program. The height of the apex of the prism above the centerline of the test pipe ( "h" in Figure A-2) must be changed when changing prisms for data acquisition. The angle 4 referred to in the prism analysis (Appendix A) is the angle "ANG", in degrees, of this computer program. The easiest method of determining this angle is to locate two particle image paired series, one for a particle in the lower section of the pipe and one for a particle in the upper part, which are located on the pipe wall and vary the angle until the program locates both on the pipe wall. Misalignments of up to 5' are very difficult to detect and are nearly impossible to measure accurately. At the completion of this section of the program, the reconstructed particle paths are expressed in cylindrical coordinates with noise included.
The position error or noise from the digitization process is random in amplitude up to the coordinate maximum errors discussed in section 4.1 and 4.2 and in all frequencies through half the cinematographic recording rate. The position errors at higher frequencies are eliminated from the reconstructed particle paths by using a digital filter. First, the particle path position data are transformed into Fourier coefficients in the frequency domain. The transformation is accomplished by using a Fourier series of sine functions and varying the amplitudes of their coefficients until the resultant series exactly matches the reconstructed
particle path. This accomplished by using a Fast Fourier Transform (FFT) for sampled particle paths. The frequency domain is a plot of the coefficients against their corresponding frequencies. The coefficients above a predetermined frequency are set equal to zero. The remaining terms are transformed back into the time domain using an inverse FFT to yield reconstructed particle paths with no frequencies present above the predetermined frequency which is the cutoff frequency for the data. An interesting observation is that data can be totally obscured by noise but providing the noise is of a different frequency than the data,:it can be removed or digitally filtered out leaving only noise free data. This procedure of transforming the reconstructed particle paths into the frequency domain, filtering out the frequencies above the cutoff frequency, and transforming back into the time domain is the type of digital filtering that is used in this program.
This digital filtering is a simple procedure to eliminate the higher frequencies of noise but before using it, the pitfalls must be known. The sample time increments must be equal. This is automatically accomplished since the cinematographic recording rate is constant and, thus, the time interval between frames (sample time increment) is constant. The highest frequency in the data must be at or below half the cinematographic recording rate (folding frequency) in order to eliminate "aliasing" which occurs when high frequency components of a time function match low frequencies if the sampling rate is too low. The highest frequency noise that can be induced in frame by frame data entry is at the folding frequency so noise cannot be "aliased". The cinematographic recording rate must be high enough to insure that the highest frequency of the turbulence is below the folding frequency to eliminate turbulence frequency "aliasing".
Thus, sampling must be at a rate at least twice as high as the highest frequency present in the turbulent fluctuations. This digital filter is equivalent to multiplying the Fourier coefficients by a rectangular function of unit amplitude up to the cutoff frequency. This rectangular function multiplication in the frequency domain is equivalent to performing a convolution with the function (sin t)/t in the time domain. This function does not go to zero but has side lobes which cause oscillatory variations on the ends of the filtered particle path reconstruction. The oscillations are a small percentage of the amplitude of each end of the reconstructed particle path that is processed through the FFT program and rectangular filter. This truncation error was reduced to a minimum for the rectangular filter by fitting a line through the end points of each sampled particle path, and processing only deviations from that line in order to reduce the amplitude of the time domain data. A plot of selected reconstructed particle paths with and without filtering shows that phase shift is not a problem. When the filtered frequencies are the higher frequencies in the spectrum, the filtered particle path reconstruction appears smoothed much the same as if it were subjected to a polynomial smoothing formula.
In the second section of the computer program the higher frequency
noise is removed from the data using a digital filter in conjunction with the Fast Fourier Transform (FFT) program written by Robinson, 1967. The digital filter is entered by calling the subroutine "FILTER" in line 84 of the main program in Figure 4.5. The data areprocessed one reconstructed particle path at a time with the filter using the cylindrical coordinates of the reconstructed particle path data points ( x, rad, theta), the number of data points in the particle path (JTOT), and the cinematographic
recording rate (RATE) as its working data. Before the data are transformed to the frequency domain for filtering, the linear trend information is removed by constructing a straight line between the unfiltered particle path end points and processing only the deviations from this line through the FFT program and the digital filter. By eliminating the trend information from consideration in this manner, the amplitudes of the end points of the modified particle path data processed through the filter are zero which reduces the filter error at the ends of the filtered particle path reconstructions that results from truncation of the Fourier series when using a square filter. The FFT program is entered at this point with the trend removed data by calling the subroutine "NLOGN" for each of the three coordinates in lines 41, 42, and 43 of the subroutine "FILTER". The transformed data are returned to the subroutine "FILTER". The highest retained frequency is set by altering line 44 of this subroutine. For this work, 6 Hz was the maximum retained frequency (see section 5.1). The data, now in the frequency domain, have the amplitudes of all frequencies above 6 Hz set equal to zero which eliminates the higher frequencies in the data. The data are transformed back to the time domain by calling the subroutine "NLOGN" in lines 60, 61, and 62 which are inverse transforms. The digitally filtered fluctuating data are recombined with the trend information and returned to the main program. The now filtered particle path data can be used with a much higher degree of confidence since the noise above 6 Hz has been eliminated. If temporarily by-passing the digital filter becomes necessary, it can be accomplished by replacing "go to 117" with "go to 2000" in line 35 of the main program.
62
The velocities of the particles can be calculated at each data point in the reconstructed particle paths. The three components of velocity are calculated for both the cylindrical and Cartesian coordinate systems since both will be utilized in later programs. A three data point calculation of velocity is used since it approximates the reconstructed particle path by a parabola from time t1 to time t3* This method approximates a parabola only if the time increments are equal as is the case in this work. The velocity components of point (i) are calculated by using the equations,
( i+1- Xi_1)
Oxi = ti+1 - ti_1)
( Ri+l R i_1
(ti+1 t il1
Ri(6i+1 - el_1)
Ui (ti+I - ti_)
where Uxi is the instantaneous axial velocity, URi is the instantaneous radial velocity, U 0 is the instantaneous circumferential velocity, and (Xi, Ri, 6i, ti) are the cylindrical coordinates and time at reconstructed particle position (i). With the positions and velocities determined at the data points, the average velocities and root-mean-square velocities can be calculated.
In the final section of the computer program, the average and rootmean-square velocities are calculated for the time and space-fixed volume observed in this work. These quantities are determined at radial increments. The assumption is made that these turbulent flow quantities only have a radial dependency. The flow volume viewed through the prism is
63
divided into shells which have a radial thickness of 2% of the radius. One of the shells is shown in Figure 3.2. The velocities are summed for all reconstructed particle positions in each shell for a spatial total, and over time fora space-time total which is then divided by the number of data points in the space-time shell to yield space-time average velocities. An identical summing procedure is used for the squared velocities which are needed to calculate the turbulent intensities or root-mean-square velocities. The average velocities and turbulent intensities are computed using the equations,
K
z Ux
i=l
UX
K
K
E. U i i=l
R K
K
E U0i =: i=l
K
K 2
2
U X UXRMS K - x
-E~ U Ri U i=li
RRMS K
K 2 i-= ei ORMS K
where ( U-, UR, U0) are the cylindrical components of the average velocity for a shell, (UXRMS, URRMS, UORMS) are the turbulent intensities or root-
mean-square velocities for a shell, and K is the total number of data points utilized in the shell calculation.
The output from this program is average and root-mean-square velocities, and instantaneous reconstructed particle path positions and velocities. The instantaneous positions and velocities are recorded on computer print-out and cards at the reconstructed particle path data points. The information is needed in this order for use in constructing a visual display of the reconstructed particle paths, but particle path data positions must be grouped by frame for use in constructing visual displays of instantaneous velocity fields and referencing the data to a fixed grid into which the studied flow volume may be referenced. A copy of the computer cards arranged by frame is made using a simple computer program. This program is listed in Figure 4.6 for continuity of the method of data reduction.
224-FOLLOW -FORT -SYSPR [NT
LEVEL 2.1 ( JAN 75 )
0S/360 FORTRAN H EXTENDED
DATE 76.251/15.
REQUESTED OPTIONS: NODECK,NOLOAD*OPT=0,LC(48) OPTIONS IN EFFECT: NAME(MAIN) NOOPTIMIZE LINECGUNT(484 SIZECMAX) AUTODBL(NONE) SOURCE EBCDIC NOLIST NODECK NOOBJECT MAP NOFORMAT GOSTMT NOXREF ALC NOANSF NOTER
ISN 0002
ISN 0003
ISN 0004 ISN 0005
ISN 0006 ISN 0007 ISN 0008 ISN 0009 ISN 0010 ISN 0011 ISN 0012 ISN 0013 ISN 0014 ISN 0015 ISN 0016 ISN 0017 ISN 0018 ISN 0019 ISN 0020 ISN 0021 ISN 0022 ISN 0023 ISN 0024 ISN 0025 ISN 0026 ISN 0027
ISN 0029 ISN 0030
C THIS PROGRAM FINDS SMOCTHED POSITION AND VELOCITY WITH AVERAGE C VELOCITIES AND RMS VALUES BY SHELLS C READ, DATA INTO COMPUTER AND SET UP HEADINGS FOR OUTPUT
REAL NA.NG.ZB(64),ZE(64),X(64),Z(64),Y(64).RA)(64),THETA(64)
1VELX(64)vELR(64) .VELT(64), NW
DIMENSION .IX (64),liZB(64).IZE(64),VELY(64),VELZ(64)oD(64),E(64),
IF( 64)
COMPLEX A(64) 9 B(64)gC(64)
DIMENSION SUMU(28)- SUMV(28JSUMW(281.SUMUU(28),SUMVV(28),SUMIW(2B)
IRATRO(28) .KI(23).UAVG(28)-VAVG(28) , /AVG(28) ,URMS(28) *VRMSt28) ) IWRMS(28) .fRATUUA(29)RATVUA(29)RATWUA(29),RURMS(29),RVRMS(29 ,
IRWRMS( 29)
C SET INITIAL VALUES TO ZERO
DO 1-0 I=1,57
SUMU(I )=0 SUMV ( I )=0 SUMW (I )=0
SUMUU( I)=0 SUMVV( I)=0 SUMWW( I )=0
KI(I)=0
10 CONTINUE SUO=O SVO=O
SWO=O
TUR S= 0.
TVRMS=O.
TWRMS=O.
READ(5,100) JRERATESCALEHSCALEVTEMPIDATEsXZEROZBZEROZEZERO 100 FORMAT( 14,2XF4.142XF64,2X9F6.4,2XF4.1.2X16.3(2XFS.1)) WRITE(6,IO1) JRE, TEMP. IDATF
101 FORMAT(IH1.1OXI6HREYNOLDS NUMBER=.142HAT9F4*192HONtI6,/////) 102 READ(5s103) IPART,.J 103 FORMAT(I4,2XI4) IF(IPARTEQO0)GO TO 109
C JRE=REYNOLDS NUMBER, RATE=FRAMES PER SECOND, SCALE=MAGNIFICATION
C RATIO OF FILM PRISM TO TRUE PRISM, IPART=PARTICLE, ZBZERO ZEZERO
C ZERO ARE INITIAL VALUES OF ZB ZE X,- J=FRAMES
WR.ITE( 6,104)
104 FORMAT(9X.5HPRTCL,2X, IHI,2X,5HFRAME, aX, 1HY,8XIHZ,8X*lHX,8X lHR, I X,5HTHETA,8X, 2HUX,8X,22HVR,8X,2HWT,8X,2HVY,8X,2.HVZ///)
FIGURE 4.5 Computer program to calculate filtered positions and velocities
MAIN OS/360 =ORTRA4 H EXTENDED
ISN 0031 JTOT=O
ISN 0032 DO 108 1=1.65
ISN 0033 READ'(5,105) IX(1),IZB(1),IZE(I)
ISN 0034 105 FORMAT ( 14,1313,.2X)
[SN 0035 IF(IX(I),EQ.OAND.IZE(I).EQ.O.ANDIZE(I)EQ.o) GO TO 117
ISN 0037 JTOT=JTOT+l
ISN 0038 IZB(I)=IZB(I)-500
[SN 0039 IZEI I)=500-IZE(I)
ISN 0040 X(I)=IX{ I)ISN 0041 ZB(I)=IZBI1)
ISN 0042 ZE(I)=IZEC.I)
C CALCULATION OF TRUE PARTICLE POSITION
ISN 0043 R=63.5
ISN 0044 NA=! 00
ISN 0045 NG=. e50
ISN 0046 NW=1.33
ISN 0047 H=110.2
ISN 0048 PI=0.78540
ISN 0049 ANG=00
ISN 0050 ZB(I)=(ZB(aI)-ZBZERO)*SCALEV
ISN 0051 ZE(I)=(ZE(I)-ZEZER0)*SCALEV
ISN 0052 X(I)=(X(I)-XZERO)*SCALEH
ISN 0053 DELTAC=ARS.IN(NA/NG*SINIPI+ANG*PI/45))
ISN 0054 DEL'AD=ARSIN(NA/NG*SIN(PI-ANG*PI/45).)
ISN 0055 TC=TAN(PI+DELTAC.
ISN 0056 TD=TAN(PI*DELTAD)
ISN 0057 U=TAN(PI)
ISN 0058 AA=TC**2I*
ISN 0059 BB=2.*TC*(H-ZB(I)*U)-2,*ZB(I)*TC**2
ISN 0060 CC:{H-ZB(I)} U)**2-R*2-2,*ZB(I)*TC*(H-ZB(I)*U) ZB{I)**2*TC*2
ISN 0061 ZC=C-8+SQRT(BB*BB-4o*AA*CC))/(2.*AA)
ISN 0062 DD=TD**2+1,
ISN 0063 EE=-2.*TD*(H-ZE(I)*U)+2.*ZE(I)*TD**2
ISN 0064 FF=(H-ZE( )*U)**2-R**2-2e*ZE(I),,TD*(H-ZE(I)*UI+ZE(I)**2*TD**2
ISN 0065 ZD=(-EE-SaRT(EE*EE-4.*DD*FFJ)/(2.*DD)
ISN 0066 VC=SQRT(R4-R-ZC*ZCk
ISN 0067 VD=SQRT(R*R-ZDZD)
ISN 0068 THETAC=ATAN2(ZC,VC)
ISN 0069 THETAD=ATA;N2(-ZDVD)
ISN 0C70 GAMMAC=ARSIN(NG/NW*SIN(PI-DELTAC-THETAC))
ISN 0071 GA.AD=ARS;IN(NG/Nw*SIN(PI-DELTAD-THETADJ)
ISN 0072 WC=TAN(2.*PI-THETAC-GAMMAC)
ISN 0073 WD=TAN(2.*PI-THETAD-GAMMAD)
[SN 0074 Z(I2=(ZC*WC+ZD*WD-VC VD)/(WC+WD)
ISN 0075 Y(I)=VC+(Z(I)-ZC)*WC
C CONVERT FROM CARTESIAN TO CYLINDRICAL
FIGURE 4.5 - continued
LEVEL 2,! (,JAN 75 )
DATE 76,251/15,
OS/360 FORTRAN H EXTENDED
.ISN ISN
ISN
ISN
ISN
ISN
ISN
ISN ISN
ISN
ISN
ISN
ISN ISN
ISN ISN
ISN
ISN ISN
ISN
ISN
ISN
ISN
I SN ISN
ISN ISN
ISN ISN ISN
ISN
ISN
ISN
0076
0077 0079 0080 00a1 0C82
0083
0084 0085
0086 0087 0088
0089 0090
0091
0093 0094
0095 0096 0097
0098
0100
0102
0103
0104 0105
0106
0107 0108
0110
0111 0112
0 113
ISN 0114
ISN 0116
RAD( I)=SORT(Y4I)*Y-(I)+Z41)*Z(I))
IF(Z(I).EQ.0.0.AND.Y(I).EQ�0,0) GO TO 113
TH;TA( I)=( ATAN2(Z( I)Y( I)) )*45./PI
GO TO 115
113 THETA(I)=0.0
115 CONTINUE
108 CONTINUE
C FILTER NOISE OUT 117 CALL FILTE-R(XRADTHETA*JTOT.RATE) 2000 CONTINUE
C CONVERT FROM CYLINDRICAL TO CARTESIAN
DO 112 I=IJTDT
Y( IJ=RAD(IJ*COS(THETA(I )*PI/45.3 Z(I)=RAD(I)*SIN(THETA(I)*PI/45P4 112 CONTINUE
DO 118 I=1JTOT
C CALCULATION OF VELOCITIES
IF(I.LE,2JGO TO 1:14
V-LX(I-1)=(X(I)-X(I-2))*RATE/2.
VELR(I-1)=(RAD(I)-RAD(I-2))*RATE/2*
VELT(I-1)=(THETAI )-THETA(I-2))*RAD(1-1)*PI/45.*RATE/2.
VELV(I-I)=(Y(I)-Y(tI-2))*RATE/2.
VELZ(I-1)=(Z(I)-Z(I-2)) *RATE/2*
C THIS WILL CORRECT VELT ACROSS THETA= 180.0
IF((THETA(I)-THETA(I-2)),GT,180,0 VELT(I-I)=-VELT(I-1)+
1(6,28319*RAD(I-1)*RATE/2,l
IF((:THETA( I)-THETA(I-2)).LT,-180.0 VELT(I-1)= VELT(I-1)+
1(6�28319*RAD(I-1J*RATE/2,) 114 CONTINUE
C VELOCITIES ON FIRST POSITION SET EQUAL TO ZERO BUT DO NOT USE
VELX(I )0.
VELR (1)-=0.
VELT( 1 )=0.
VELY (1 )=0 VELZ( I)=0,
IF(I*EQI)GO TO 107
K=I-1
L=J- 1
WRITE(6,106) IPART9 K, L, Y(K), Z(K), X(K), RAD(K). THETA(K),
IVELK(K), VELR(K), VELT(K),VELY(K), VELZ(K),
106 FORMAT( 113, 1417.Fi2.2,F9.2,Fg.2.F9.2,FlX.2,5(FIO.2))
C THIS SECTICN WILL YIELD AVERAGE VELOCITIES AND RMS VELOCITIES
C RATIO 0= RADIUS OF DATA POINT TO PIPE RADIUS TO YIELD FRACTION OF C RADIUS OF PIPE THE DATA POINT IS IN FROM THE WALL
IF(I.EQo2) GO TO 107 RATIOR=I .-RAD(K)/63.5
FIGURE 4.5 - continued
MAIN
DATE 76. 251/15a
LEVEL 2.1 (JAN 75
MAIN 05/360 FORTRAN H EXTENDED
ISN 0117
ISN 0118 ISN 0119 ISN 0121 ISN 0122 [SN 0123 [SN 0124 ISN 0125 ISN 0126 ISN 0127
ISN 0128 ISN 0129 ISN 0130 [SN 0131
ISN 0132
ISN 0133 ISN 0134
ISN 0135 ISN 0136 ISN 0137 ISN 0138 ISN 0139 ISN 0140 ISN 0141 ISN 0142 ISN 0143 ISN 0144 ISN 0145
ISN 0146 ISN 0147 ISN 0148
ISN 0149 ISN 0150 ISN 0151 ISN 0152 ISN 0153 ISN 0154
ISN 0155 ISN 0156 ISN 0157 ISN 0158
DO 20 M=1,28
C ESTABLISH SHELL CENTERS AT 2% INCREMENTS AND CHECK DATA POINT IN SHELL
RAT (OM)=(M-I)*0,02+0,010
IF(RATIORLT.,(RATRO(M)-0.010).OR.RATIORGT.CRATRO(M)+00,O))GOT020
SUMU(M)=SUMU(M)+VELX( K)
SUMV(M4)=SUMV(M)+VELR( K) SUMW ( M )=SUMW (M)+VELT(K)
SUMUU(M)=SUMUU(M)4VELX(K)*VELX(K) SU V (M)=SUMVV(M) .VELR (K) * VELR (K) SUMWW( M)=SUMWW( M)+.VELT (K)*VELT (K)
KI( M)=KI(M)+1 20 CONTINUE 107 J=J*1 118 CONTINUE 110 WRITE(6,111) III FORMAT(/} GO TO 102
109 DO 30 J=1,28 C AVERAGE VELOCITIES AT THE SHELL LOCATIONS
IF(Kl{J) ) 11,11,12 11 UAVG(J)=O VAVG(J )=0 WAVG( J)=O URMS( J)=O
VRMS(J )=O WRMS ( J) =0 GO TO 13
12 UAVG(J)=SUMU(J)/KI(J) VAVG(J)=SUMV(J)/KI (J) WAVG( J )=SUMW(J)/KI (J)
C RMS VELOCITIES AT SHELL LOCATIONS
URMS(J)=SQRT(SUMUU(J/Kl(J)-UAVG (J2*UAVG(J))
VRMS(J)=SQRT(SUMVV(JJ/KI(J)) WRMS(J)=SQRT(SUMWw(J)/KI(J))
C
13 SUO=SUO+UAVG(J) SVO=SVO+VAVG( Ji SWO= SWO+WAVG (J)
TURMS=TURMS+URMS(J) TVRMS=TVRMS+ VRMS( J) TWRMS=TwRMS+WRMS(J)
C UA IS PIPE AVERAGE VELOCITY IN MM/SEC
UA=29. 1
RATUUA( J)=UAVG( J )/UA RATVUA(J)=VAVG( J)/UA RATWUA(J)=WAVG( J)/UA
FIGURE 4.5 -,continued
LEVEL 2e1 ( JAN 75 )
DATE 76o251/15
MAIN OS/360 FORTRAN H EXTENDED
ISN 0159 RURMS(J)=URMS(J)/UA
ISN 0160 RVRMS(J=VRMS(JJ/UA
ISN 0161 RWRMS(J)=WRMS(J)/UA
ISN 0162 30 CONTINUE
C CALCULATE AREA AVERAGE VELOCITIES (UJVOWO)-28.IS NJ. OF SHELLS ISN 0163 UO=SUO/28.
ISN 0164 VO=S VO/28.,
ISN 0165 wO=SWO/28,
C CALCULATE AREA AVERAGE RMS VALUES ISN 0166 AURMS=TURMS/28.
ISN 0167 AVRMS=TVRMS/28.
ISN 0168 AWRMS=TWRMS/28,
C
ISN 0169 WRITE(69200) UO.VO.WO
ISN 0170 200 PORMAT(H1.l0X*35HTHE AREA AVERAGE VELOCITIES ARE UO=,F6,2,4X,3HVO
1=,F6,294X. 3HWO=,F6.2 9//) ISN 0171 WRITE(6,201)
ISN 0172 201 FORMAT (5X9 3HY/R , 5X, 5HUXAVG, 5(, 5HVRAVG9 5X. 5HWTAVGp 6X, 5HUXRMS,9X SHV
1RRMS5Xv5HWTRMS 10X.3HNO- ./i
ISN 0173 WRITE(6,202) (RATRO(J) UAVG(J)tVAVG(J).WAVG(J),URMS(J)tVRMS(J).j
IWRMS(J).KI(J),RATUUA(J)}RATVUA(J),RATWUA(J),RJRMS(JJ.RVRMS(J}
1RWRMS(J)vJ=ts28)
ISN 0174 202 FORMAT (4.XF5 .3,4X.F5.2.5XF5.2,5XF5.2. 5XF62,4X, F6.2,4XF6.2.8X,
114,q'X 6F8o-3)
ISN 0175 WRITE(6,203) AURMSAVRMSAWRMS
ISN 0176 203 FORMAT(////,IOX*38HTHE AREA AVERAGE RMS VALUES ARE AURMS=tF6s294X9
16HAVRMS= 9F 6e2*4Xg(6HAWRMS= 9F6 * 2) ISN 0177 STOP
ISN 0178 END
FIGURE 4.5 - continued
DATE 76*251/154
LEVEL 2*1 (JAN 75 )
REQUESTED OPTIONS: NODECKNOLOAD ,OPT=O,LC(48)
OPTIONS IN EFFECT: NAME(MAIN) NOOPTIMIZE LINECOUNT(48) SIZE(MAX) AUTODBL(NONE) SOURCE EBCDIC NOLIST NODECK NOOBJECT MAP NOFORMAT GOSTMT NOXREF ALC NOANSF NOTE
ISN 0002 SUBROUTINE FILTER(XRtTHETAeJRATE)
ISN 0003 DIMENSION X(64),R(64),THETA(64).D(64.E(64)sF(64)
ISN 0004 COMPLEX A(64),B(64),C(64)gWK*HOLD*Q
C THIS SECTION FILTERS HIGHER FREQJENCY NOISE OUT OF DATA USING FASTC FOURIER TRANSFORM METHOD
ISN 0005 3 IF(UJLE*2) N=I
ISN 0007 IF(JGT.24AND.J*LE,4) N=2
ISN 0009 IF(J.GT,4.AND*JLE.8) N=3
ISN 0011 IF(U.GT.8,AND*J*LE.16) N=4
ISN 0013 IF(JGT�I6,ANDJ.LE,32) N=5
ISN 0015 IF('J*GT.32eAND*J.LE*b4) N=6
[SN 0017 K=J+1
ISN 0018 L=2**N
C USE END-POINTS OF SERIES DATA FOR STRAIGHT LINE TO ELIMINATE SIGNAL
C OF GROSS MOV.MENT OF PARTICLE FROM FOURIER CONSIDERATION
ISN 0019 XSLOPE=(XJ)-X(l))/(J-1)
ISN 0020 RSLOPE=(R(J)-R(1))/(J-1)
[SN 0021 THETAS=(THETAJ)--THETA(1))/(J-I,}
ISN 0022 XBEG=X(1)
ISN 0023 RBEG=R(1)
ISN 0024 THETAB=THETA(1)
ISN 0025 DO 5 1=1,J
ISN 0026 XO=XSLOPE* (I-I )+XBEG
ISN 0027 RO=RSLOPE*(I-Ii+RBEG
ISN 0028 THETAO=THETAS*(I-I)+THETAB
ISN 0029 A(I3=X(I)-XO
ISN 0030 8(I)=R(1)-RO
ISN 0031 C([I=THETA(I)-THETAC
ISN 0032 5 CONTINUE
ISN 0033 DO 1 I=KL
ISN 0034 X(Ij=O.
ISN 0.035 R(I)=0.
ISN 0036 THETA(I)=0.
ISN 0037 A(I)=0.
ISN 0C33 B(I=O .
ISN 0039 C(I4=0.
ISN 0040 1 CONTINUE
ISN 0041 CALL NLOGN(N,A, 1.0)
ISN 0042 CALL NLOGN(NB,.10)
ISN 0043 CALL NLOGN(N,C,1.0)
C FILTER OUT FREQUENCIES ABOVE 'FREG"
FIGURE 4.5 - continued
O5/360 PORTRAN H EXTENDED
DATE 769251/15
LEVEL 2*1 ( JAN 75 )
LEVEL 2.1
ISN 0044 ISN 0045 ISN 0046 ISN 0047 ISN 0048 ISN 0049 ISN 0051 ISN 0052 ISN 0053 ISN 0054 ISN 0055 ISN 0056 ISN 0057 ISN 0058 ISN 0059 ISN 0060 ISN 0061 ISN 0062
ISN 0063 ISN 0064 ISN 0065 ISN 0066 ISN 0067 ISN 0068 ISN 0069 ISN 0070 ISN 0071 ISN 0072 ISN 0073 ISN 0074 ISN 0075 ISN 0076 ISN 0077
0S/360 =nRTRAN H EXTENDED
FREQ=6.
IDELTA=L/2*( 1 ,-FREQ*2,/RATE)
LL ItI=L/2+1 -IDELTA UL I M=L/2t 1+ DELTA
DO 4 I=1,L
IF(I.LE.LLIM.OR.I.GE.ULIM) GO TO 4
A( I,)=0.
B(1)=O.
C(I3=0.
4 CONTINUE
DO 5; 1=1 ,L
D(I)=CABS(A( I))**2 E (I)CABS( B( I))**2 F(1) =CABS(,C( 1))**2
6 CONTINUE
CALL NLOGN(NA,-l0) CALL NLOGN(NB*-Io0) CALL NLOGN(N,C9-.0)
DO 7 1=19J
XO=KSLOPE* (I-1) +XBEG RO=RSLOPE*(I-1)+RBEG
THETAO=THETAS*( I-I )+THETAB
X( I.)=A( I )+,XO R( I)=B(I)+RO
THETA(1)=C(I)+.THETAO
7 CONTINUE
DO 8 I=KL
X(I.=A(I)
R(1)=B(I)
THETA( I)=C(U)
8 CONTINUE
RETURN
END
FIGURE 4.5 - continued
DATE 76o251/15
( JAN 75)
FILTER
REQUESTED OPTIONS: NODECK*NOLOADDPT=O,LC(48) OPTIONS IN EFFECT: NAME(MAIN) NOOPTIMIZE LINECOUNT(481 SIZE(MAX) AUTODBL(NONE) SOURCE EBCDIC NOLIST NODECK NOOBJECT MAP OFORMAT GOSTMT NOXREF ALC NOANSF NOTE
ISN 0002
ISN 0003
C
ISN 0004 ISN 0005 ISN 0006 ISN 0007 ISN 0008 ISN 0009 ISN 0010 ISN 0011
ISN 0012 ISN 0013 ISN 0014 ISN 0015 ISN 0016 ISN 0017 ISN 0018 ISN 0019 ISN 0020 ISN 0021
ISN 0022 ISN 0023 ISN 0024 ISN 0025
ISN 0026 ISN 0027 [SN 0028 [SN 0029
ISN 0031 ISN 0032 ISN 0033 ISN 0034 ISN 0035 ISN 0037 ISN 0038 ISN 0039
FIGURE 4.5 - continued
SUbROUTINE NLOGN(NX,SIGN)
FFT ROUTINE BY ROBINSON-1967 .NMA)X=LARGEST VALUE OF N TO BE PROCESSED NONDUMMY DIMENSION M(NMAX.) FOR EXAMPLE, IF NMAX=6 THEN DIMENSION M(6) DIMENSION X(2**N) DIMENSION X(64) COMPLEX X-PWKgHOLD*Q LX=2**N DO I I=1,N
1 M(I=2**(N-I) DO 4 L=IN NBLOCK=2** (L-1) LBLOCK=LX/NBLOCK LBHALF=LBLOCK/2 K=O
DO 4 IBLOCK=19NBLOCK FK=Ki
FLX=LX V=S GN*6.2831853*FK/FLX WK=CMPLX(COS(V)vSIN(V)) ISTART=LBLOCK*( IBLOCK-1) DO 2 I=1,LBHALF J= I START+ JH=J +LBHALF
Q=X( JH)*WK
X( JrH )=XCJ)-Q X( J)=X(J)-Q
2 CONTINUE DO 3 I=2,N 11=1
IF(K.LT.M(I)) GO TO 4
3 K=K-M( I) 4 K=K+M(II) K=O
DO 7 J=l,LX IF(K.LT*J) GC TO 5 HOL)=X(J) X( J)=X(K+I)
X(K+I )=HOLD
DS/360 -ORTRAN H, EXTENDED
DATE 76o251/15
LEVEL 2*1 ( JAN 75 )
LEVEL 2.1 ( JAN 75 )
ISN 0040 5
ISN 0041 ISN 0042
ISN 0044 6
ISN 0045 7
ISN 0046 ISN 0048
ISN 0049 8
ISN 0050 ISN 0051
OS/360 FORTRAN H EXTENDED
DATE 76.251/15,
DO 6 1=1#N
IF(KLT*M(I) GO TO 7 K=K-M( I ) K=K+M( II) IF(SIGN.LT.0.0) RETURN DO B 1=,LX X( I3=X ( I)/FLX RETURN END
FIGURE 4.5 - continued
NLOGN
641-FOLLOW -FORT -SYSPRINT
LEVEL 2.1 ( JAN 75 ) CS/360 FORTRAN H EXTENDED DATE 76.239/20.
FEGUESTED OPTIONS: NODECKNOLOADCPT=O
OPTIONS IN EFFECT: NAME(MAIN ) NCCPTIMIZE LINECOLNT{74) SIZE(MAX) ALTODGL(NONE) SOURCE EBCDIC NOLIST NODECK NOOBJECT MAP NOFORMAT GOSTMT NCXREF ALC NOANSF NOTER
C PRCGAAM TO PUNCH CARDS EY FRAME
C MUST BE "COOO0 CARD AT END OF DATA INPUT
C INPUT CARDS ARRANGED BY PARTICLE, OUTPUT CARDS ARRANGED aY FRAME C I IS ATLEAST NO. OF CARDS INPUT, N IS ACTUAL NC* OF CARDS INPUl
C IFPAME IS NO. OF FRAMES USED IN ANALYSIS
ISN 0002 DIMENSION DATA(4'0020)vIATA(4000.3)
ISN 0003 N=0
ISN 0004 DO 1 1=194000
ISN 0005 READ(59116) (IDATAtIJ),J=I.3),(DATA(I.K),K=1.2C)
ISN 0006 116 FQRMAT(14q2,I2,20A3)
ISN C007 IF(IDATA(I,3),EQ*.) GO TO 2
ISN C00g N=N+I
ISN 0010 1 CONTINUE
ISN 0011 2 DO 10 IFRAME=1,55
ISN 0012 WRITE(6,101) IFRAME
ISN 0013 101 FORMAT(HI,//.30X.6HFRAME=, I4//)
ISN C014 'RI TE(6, 102)
ISN C015 102 FORMAT(9X,5HPRTCL,2X, IHI,2X,5HFRAME@a8X,IHY,8XIHZ,8X, 1FXeXIHR,
18X,5HTHETA,8X,2HUX,8X,2HVR,8X,2HWT,8X,2HVY,8X,2HVZ,///) ISN 0016 DO 20 I=19N
ISN 0017 IF(ICATA(I,3)*NEIFRAME) GO TO 20
ISN C019 IF(IDATA(1,2).EC.1) GO TC 20
ISN 0021 NPITE(6, IC) U!ATA(IJ) ,=,3), (CATA{IK), - -O
ISN 0022 106 FORMAT(I13. 14,17,6X,2A3,3X,2A3,3X,2A3,3X,2A3,5X,2A3,5(4X,2A3))
ISN 0023 WRITE(7,116) (ICATA(1,J),J=1,3),(DATA(I,K)K=1,20)
ISN 0024 20 CONTINUE
ISN 0025 10 CONTINUE
ISN 0025 STOP
ISN 0027 END
4N
FIGURE 4.6 Computer program to rearrange data by frame
4.5 Referencing Data to a Grid
The three dimensional positions and velocities computed in the
previous section can be used for analysis and display or can be processed through a position referencing procedure to yield velocities at regular intervals in the flow field. The computer program to reference the velocity field to specified fixed geometric grid locations in the flow field is listed in Figure 4.7. Plane views can be constructed since the reference locations lie on regularly spaced planes. The number of reference or grid locations can be altered for clarity of display with relatively little effort. Nonuniform data locations that change from frame to frame must be studied much more closely to understand the changing velocity field. Caution should be exercised when using any system which interprets velocities at random locations to predict velocities at grid locations since it necessarily smooths the velocity field. This type of interpretive system should only be used in conjunction with nonreferenced data displays in order to see what effect the procedure has on the appearance of the velocity field. Any grid referencing system must necessarily apply some kind of a weighted average of the velocities over a predetermined volume of influence. This has the tendency to smooth the velocities, suppressing the velocity gradients and shear stresses. If large strain variations over short distances are present in the flow field, these variations will also be reduced. The result can be that a highly irregular velocity field may appear as a relatively regular and smooth velocity field.
The referencing grid boundaries for this work range from 63.5 to 35.5 mm in the radial direction, 280 (+ 140) in the circumferential direction, and 10 to 38 mm in the axial direction. The grid reference
positions are constructed at the intersections between radial planes every 1.27 mm from each other, azimuthal planes every 2� of arc, and axial planes every 4 mm of axial length. A 4 mm radius spherical volume is digitally constructed around each reference position. The velocities of all data points located within this volume are considered to be correlated to the velocity of the fluid at the reference position, and inversely, the velocity of the fluid at the reference position is correlated to the velocities of the data points in the volume. The amount of influence each of these velocities has on the reference position fluid velocity is based on the distance of the data point from the center of the sphere which is the reference position. The reference position velocities are determined by the equations,
N
E (U xi * WTFi) i=l N
UX N
E WTF.
i=l
N
E (URi WTFi) U Ri=l UR N
E WTF.
i=l
N
E (U0i � WTFi) = i=l 0 N
Z WTF.
i=l 1 where WTF is the weight factor and N is the number of data points within
4 mm of the reference position. The assumption has been made that the velocity of a data point at the reference position would have the most
influence on the grid or reference position fluid velocity, while a point 4 mm away would have no influence, and that there was a linear decrease in influence. Thus, the weight factor was determined by the expression,
WFT (4-radius)
4
where "radius" is the distance between the data point and reference point in millimeters. The reference positions closer to the pipe wall than 4 mm have a skewed data problem that must be resolved. This is done by adding a zero magnitude velocity vector at the same distance from the reference point as the data point if the data point is further from the reference point than the pipe wall is. This alleviates the skewed data problem at the pipe wall by reducing the biasing influence of the data point.
There should be a minimum of 2 or 3 data points in each volume of influence or approximately 8 data points per cubic centimeter. This means that in the 30 cm3 volume of this reference grid influenced area, 240 data points are necessary. The small prism viewing volume is approximately 50 cm3 so 400 data points or particle positions per frame of cinematographic film are needed in the volume to use the reference grid. This is 800 images on each cinematographic film frame which is four or five times the data density of this work. This is the main reason that this program was not used. It was mentioned earlier that reworking the program for following particle images and matching image pairs should be capable of such an increase in data density.
216-FOLLOW -FORT -SYSPRINT
LEVEL 2.1 ( JAN 75 )
05/360 FORTRAN H EXTENDED
DATE 76*251/15.
REQUESTED OPTIONS: NO)ECKNOLOADOPT=OLC(48) OPTIONS IN-EFFECT: NAME(MAIN) NOOPTIMIZE LINECOUNT(48) SIZE(MAX) AUTODBL(NONE) SOURCE EBCDIC NOLIST NODECK NOOBJECT MAP NOFORMAT GOSTMT NOXREF ALC NOANSF NOTER
ISN 0002
ISN
ISN ISN
ISN
ISN
ISN ISN ISN
ISN ISN
ISN
ISN
ISN ISN ISN
ISN
ISN ISN I SN ISN
ISN ISN
ISN I SN ISN
I SN
I SN ISN I SN
I SN
0003
0004 0005 0006
0007 0008
0009
0010 0011 0012
0013
0014 0015
0016 0017
0018
0020 0021 0022 0023 0025 0026 0027
0028 0029 0030
0031
0032 0033
0034
C THIS PROGRAM WILL REFERENCE THE DATA TO A GRID SYSTEM IN THE PIPE
DIMZNSION RATRO(23),THETAO(16)XO( 9)vADDU(2315, 9),ADDV(23,16, 9.
L),AD.DW(23.s16, 9)*SUMWTF(23P16, 9),U(.23916.9 9),V(23,16. 9)vW(239169
1 9)
C SET INITIAL VALUES TO ZERO
DO 40 J=1,923 DO 41 K=1,16 DO 42 L=1.)9
ADDU( JvKtL)=OO ADDV(JvKDL)=00 ADDW( JK,L)=0O
SUMWTF(J ,K *L )=O .O 42 CONTINUE 41 CONTINUE 40 CONTINUE C THE INITIAL VALUE OF IFRAM IS THE FIRST VALUE OF IFRAME
IFRAM=2
C READ IN DATA CARDS
DO 50 I=1,o4000
READ(59105) IPART, IFRAME*XR*THETA*UXVR*WT 105 FORMAT(147,2Xv12,12X,6F6.2) RATIOR=I .-R/63.5
C THIS PART ORDERS BY FRAME 86 IF(IFRAME.EQ.IFRAM) GO TO 88 C SOLVE FOR VELOCITIES AT THE GRID POINTS
00 90 J=1,22 DO 9,1 K=IS,15 DO 92 L=1,8
IF(S1UMWTF1JqKL),EGe3*0) SUMWTF(JK,L)=1I
U(J.KL)=ADDU(JKL)/SUMWTF(JoKL) V(J, KL)=ADDV(-JK.L)/SUMWTF(JKL)
W(J, K,L)=ADDW(J.K.L)/SUMWTF(J.KL) 92 CONTINUE 91 CONTINUE 90 CONTINUE C OUTPUT BY FRAME AND X WITHIN FRAMES
DO 94 L=198
WRITE(6v16) IFRAM.XG(L)
106 FORMAT(IH1,i0X,37HVELOCITY COMPONENTS =OR R=3500 FRAME=,12,2X,2HX=
1 ,F4.1 )
WRITE(6,107)
FIGURE 4.7 Computer program to reference velocity field to known locations
MAIN: 0S/360 FORTRAN H EXTENDED
ISN
ISN
ISN ISN
ISN
ISN
ISN
ISN
ISN ISN ISN
ISN ISN
ISN ISN
ISN ISN ISN ISN
ISN ISN
ISN
ISN
ISN
ISN
I SN
ISN
0035 0036 0037 0038 0039
0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 0051 0052 0053
0054 0055 0056 0057
0058 0059 0060 0061
0062
ISN 0063 ISN 0064 ISN 0065 ISN 0066 ISN 0068 ISN 0069
ISN 0070 ISN 0072 ISN 0073 ISN 0074 ISN 0076 ISN 0077 ISN 0078 ISN 0079 ISN 0080
FIGURE 4.7 - conti
107 FOR% AT ( IX, 3HY/R, 42X, 5HTHE TA) WRITE(6,108) (THETAO(K),K=1,5)
108 FOR4AT(12XF5.l,12XF5. 112XF5.112XF51 ,12XF5o 1) WRITEC6s109) (RATRO(J), (U(J.KL),V{J.KJL),W(JKL).K=1,5).J=1,22) 109 FORMAT(IX,F4.2,IX,IH( 3F51,1H),LH(.3F5,liIIH(,3F5,IvlH),IH(,3F 15., 19H), IH(, 3F5*I 1 IH))
WRITE(6,110) 110 FORMAT(/)
WRITE(6,108) (THETAO(K),K=6910)
WRITE(6,109) (RATRO(J). (U(JKL),V(J,K,L),W(JKL),K=6, 10),J=1,22)
WRITE(6. 110)
WRITE(6,108) (THETAO(K),K=119 15)
WRITE{ 61, 09) (RATR( (J) ,(U(Ji,K,L),V{ J*K,L),W(JtKL)*K=11, 15},J=1,22) 94 CONTINUE IFRAM=IFRAM*1
IF(IPART*EQ.O) GO TO 93 87 00 43 J=1,23 DO 44 K=I 16 DO 45 L=14 9
ADDU ( J, K, L )=0 .0 ADDV( J,K.L)=OO ADDW( JKL)=0*0
SUMWTF(JKL)=O .O 45 CONTINUE 44 CONTINUE 43 CONTINUE GO TO 86
88 CONTINUE C THIS PART WILL FIND GRID THAT DATA POINT INFLUENCES AID ADD THE C WEIGHTED VELOCITIES
DO 60 J=1,22
RATRO(J)=( J-1 )*0.02+0.02
RO=( 1-RATRO(J))'*63.5
IF(RLT�(RO-5eO),OR.R.GT.(RO+5.01) GO TO 60
DO 70 K=1 15
THETAO(K)r16 .-2.*K
C THIS IS 5.5MM AT 1/2R AND 11MM AT R(63.5)
IF(THETA.LT�ITHETAO(K)-10).ORTHETA.GT.(THETAO(K)+10.)) GO TO 70
O0 30 L=1,8
XO(L) =L*4.+5.
IF(X.LT.(XO(L)-5,i.OP.XeGT.(XO(L)+5.)) GO TO 80
H=O
DX=XO( L)-X
DRH=RO*SIN(THETAO(K)*I.570795/90.)-R*SIN(THETA*1.570795/90,} DRV=RO*COS(THETAO(K)*1 .570795/90. )-R*CDS(THETA*1,570795/90,
RADIUS=SQR. (DX*DX+DRV*DRV+DRHDRH)
nued
LEVEL 241 ( JAN 75 )
DATE 76*251/15
MAIN OS/360 FORTRAN H EXTENDED
ISN 0081 IF(R.ADIUSGT,4.O) GO TO 80
ISN 0083 IF((RO-R),GT,(63.5-RO)) H=(4-RADIUS)/4.
ISN 0085 WTF=(4.-RADIUS)/4.
ISN 0086 ADDU(J,K,L)=ADDU(JK,L)+UX*WTF
ISN 0087 ADDV(JK,L)=ADDV(J,K,L)+VR*WTF
ISN 0088 ADDW(JK, . =ADDW(JKL)+WT*WTF
ISN 0089 SUMWTF(JtKtL)=SUMWTF(JKtL)+H+WTF
ISN 0090 80 CONTINUE
ISN 0091 70 CONTINUE
ISN 0092 bO CONTINUE
ISN 0093 50 CONTINUE
ISN 0094 93 STOP
ISN 0095 END
co
FIGURE 4.7 -continued0
LEVEL 2,1 4 JAN 75 )
�DATS 76*251/15
4.6 Method for Displaying Reconstructed Flow Fields
At this stage of the data reduction process, a variety of quantitative information is recorded about the motion of the fluid through the recorded flow field. This descriptive information is contained in the instantaneous positions and velocities of the trace particles which travel with the flow, and their time-space averaged statistical quantities. The statistical quantities are in form for analysis but the instantaneous quantities must be put into a more manageable form. The instantaneous data points or reconstructed particle path sampling points are the positions of the particles for a series of arbitrary time intervals where the cinematographic film rate determines the time intervals. Since the particle density and sampling rate are relatively high, there is a tremendous amount of data to be analyzed even for short times. The easiest method of displaying large quantities of instantaneous flow data is by graphical representation. Two graphical methods of displaying the flow field in time were chosen. The first method was plotting the velocity vectors in the fixed volume at fixed times; the second was plotting the reconstructed particle paths. The computer graphics unit was found to be a handy way to pictorially display large quantities of data since it does not require any manual operations. The graphics unit used was the fast-draw general graphics package provided by the Gould Corporation. The package consists of a number of library subroutines that are used to construct and manipulate the graphics display, and the hardware to generate the plot.
The instantaneous velocity fields are displayed at specific times using a three dimensional perspective view, five R-theta field segment views, and five X-R field segment views. This is a quick and easy method for the illustration of flow events, since there are no manual operations.
The three dimensional perspective view or volumetric display shows the entire experimental volume at any given instant in time while the R-theta and X-R segment views clear up any confusion in interpretation of velocity vector positions and orientations. The volumetric display makes two and three dimensional motions easy to visualize since it is not necessary to assimilate the instantaneous flow field from several two dimensional plane views. Since only the volumetric view is necessary once any confusing points are resolved, it is easy to follow events in time. An example of the graphical displays drawn by this computer program are shown in Figures 4.8, 4.9, and 4.10. Methods of display that require the assimilation of several plane views are difficult to use to follow three dimensional activity in time.
The velocity field computer program, which uses the fast-draw package to construct its drawings, is constructed in three sections. The first section draws the three dimensional velocity field (Figure 4.8). The second section draws the R-theta segment velocity fields (Figure 4.9). The third section draws the X-R segment velocity fields (Figure 4.10). The second and third sections will be discussed together since their formats are the same. This discussion will be a very general flowchart of the program with emphasis on alterations for modifying the program. The complete program is listed in Figure 4.12.
The three dimensional velocity field display consists of the velocity vectors, a segment of pipe wall, and the viewed flow region boundaries. All dimensions and positions are a multiple of the actual size. This proportionality is the scale factor which is arbitrarily set by the user. The graphical representation of the flow region can be rotated to any arbitrary viewing angle by altering the rotation angles in line 7 and 8 of the program in Figure 4.12. The angles (-80' and 600) were chosen to
give the clearest view of the velocity field. Drawing the pipe section and flow region boundaries are the next operations performed by the computer. The manipulation of the "pen" (movea, linea, etc.) are the same ones that would be used when drawing the figure manually. The last operation of this section is to draw the velocity vectors. The position and velocity data are read by the computer at this point. The positions are converted from millimeters to inches by multiplying by "SCALE 1". This conversion must be made because the fast-draw routines only recognize dimensions in inches. Once the position is located, the velocity vector is drawn. Its scale is arbitrary and set by multiplying the velocity in millimeters per second by "SCALE 2". The fast-draw package does not have an arrowhead subroutine for three dimensional vectors so one was derived and programmed. The arrowheads were made proportional to the length of the vector and located in the vector-viewing vertical plane for clarity. The length is 30% of the vector with an included angle of 30�.
The R-theta and X-R plane segment views are used to clear up any
confusion in interpretation of the velocity vectors positions and orientations in the three dimensional views of the velocity field as well as to analyze flow events in two dimensions. Figures 4.9 and 4.10 are divided into five segment views and a sixth view which superimposes all the segments. The R-theta and X-R segments are 8 mm and 8� thick, respectively. The superimposing of all segments in one sketch is used to check for motions on the scale of the plane dimensions. Care must be taken when viewing the segment displays so as not to be misled by large differences in size and/or orientation of velocity vectors which are very close together in a display. The vectors may be up to 8 mm away in the
R-theta segments or 80 away in the X-R segments from each other in the direction of the normal to the plane. Segments this large were used here because of the large scale of the turbulence and relatively small quantity of data. The thickness of the segments can be varied by changing the values of "LOLIMX" and "LOLII4T". When the lower limit (lolim) equals the upper limit (uplim), the segments are reduced to planes which is necessary when using data output of the reference grid program. The lengths of the velocity vectors in the R-theta and X-R plots are calculated by multiplying the plane velocities by "SCALE 3" and "SCALE 4", respectively. The arrowheads in these sections are two dimensional counterparts of the arrowheads in the first section of this program. The two dimensional vector subroutine of the fast-draw package draws arrowheads of constant size so it was not used in the present displays.
The last computer program in the computerized data reduction method draws the three dimensional reconstructed particle path display (Figure
4.13). The input data for this program are the reconstructed particle paths from the three dimensional position and velocity program of section 4.4. This graphical display shows the motion of the fluid as it traverses the experimental volume in the test pipe. A sample of the graphical display is shown in Figure 4.11 and the complete program is listed in Figure 4.13. This display is the same section view with the same ability to be rotated as the three dimensional velocity field display. The particle paths are constructed by connecting the particle path sampling points with straight lines. "SCALE 1" converts the dimensions of the positions from millimeters to inches so the scale of the figure and the pathlines are the same factor in the "INIT" statement's argument (line 2 in Figure 4.13).
- -I -
-9
-
/ -9
'-9
--9 r\
9
C
r
V
4#-\
K 4\y
FRPE 6
.FIGURE 4.8 Three dimensional velocity field
-9
(N
/
// / J /
X='0-I8
/
.H II I THETA :I 20 -20
0 THETR
X=314-U2
1 I
20 -20
X=18-26
-I--
X=RLL
/
THETR 20
YR 0.2
1~
71\-
-20
.FIGURE 4.9 R-a plane
/ 4 i : - / ./ . .
THETA 20::" 20
segment. velocity fields
V'
THETR 20 -20
.\
0 THETA
X=2-10
L
-2
0
0
X=26-3L
0
0,
e
� I
E
THETR=U- (-I-)
-~----~
25 X
TIETR= (-IA) - (-12)
1 25 X 5(
THETr:= (-12) - (-203
25
THETr =RLL
x I
X 50
-b- -~
-w -~
I I L
0 25 X 50 0
.FIGURE 4.10 X-R plane segment velocity fields
X 50 .0 25
Y
t
X 5
0 0"
THETA=I2-11
THETR=20-12
-A
-'5-
/
PART TCLE PATHSC
FIGURE 4.11 Three dimensional particle path display
210-FOLLOW -FORT -SYSPRINT
LEVEL 2.1 ( JAN 75 ) OS/360 =ORTRAN H EXTENDED DATE 75.251/15
REQUESTED OPTIONS: NODECK9NOLOAD9OPT=0LC(48)
OPTIONS IN EFFECT: NAME(MAIN) NOOPTIMIZE LINECOUNT(48J SIZE(MAX) AUTODBL(NONE) SOURCE EBCDIC NOLIST NODECK NOOBJECT MAP NOFORMAT GOSTMT NOXREF ALC NOANSF NOTE
C FAST-DRAw PROGRAM TQ PLGT VELOCITY FIELD IN PIPE (R=3500)
C IN 3-D VIEW AND PLANE CUTS (R-THETAI AND (X-R) C THIS SECTION WILL PLOT 3-D VIEW OF FLOW FIELD
ISN 0002 DIMENSION X(90).RCi90).THETA(90,UX(90),VR(90).WT(90)*RATIO(90)
C TO CHANGE SIZE OF 3-D PLOT CHANGE OFACTI IN NEXT .INE
ISN 0003 CALL INIT (ISIZE,28.o20.'FACT,23'ORIG, B.,1O.)
C LABEL THE PLOT
ISN 0004 CALL TXSIZ(.100)
ISN 0005 CALL TEXT('gFRAME 22a*)
ISN 0006 CALL TXPLT (-.75.-3.4,0.*0.)
C THE INITIAL ALIGNMENT IS A=X. B=Ys C=Z
C THE 2-D' VIEW IS THE XY PLANE
C THE XY PLANE 1S LOOKING DOWN AT THE PIPE WITH PRISM ON RIGHT
ISN 0007 CALL ROTAT (494AB.-80.1
ISN 0005 CALL ROTAT (594AC4960o)
C USING THE DIMET AND ROTAT IN COMMENT CARDS WITHOUT THE FIRST TWO
C ROTAT CARDS WILL PLOT ISOMETRIC VIEW OF PIPE FROM DOWNSTREAM SIDE
C CALL DIMET (8,1.0)
ISN 0009 CALL PERSP (9, 0-. 0.,20.)
ISN 0010 CALL XZ
C CALL ROTAT (5.9AC4.90.)
C DRAW PIPE SECTION
ISN 0011 CALL RESERV (0.0.4)
ISN 0012 CALL DEFINE (CIR (1),'CEN',0,0.3SANG', 30.'FANG',330.,'CW',
I 'RA' , 2.5)
ISN 0013 CALL DEFINE (CIR (2)P4CEN%*O.0O�.'SANGO*330. 'FANG*, 30.oCCW',
1 RA)0, 2.75)
ISN 0014 CALL DEFINE (CIR (3)9*CEN'0.,09,*SANG'. 30.,'FANG',330.'CW0,
1 *RAD�* 1.125)
ISN 0015 CALL DEFINE (CIR (4).'CEN'.C.,OoO.SANG.i330.'FANG, 30.'CCW',
I�RAD�9 1.125)
ISN 0016 CALL MOVEA (2.165,0o, 125)
ISN 0017 CAL. *DRAW (CIR (1))
ISN 0018 CALL MOVEA (2.381,0.-1.375)
ISN 0019 CALL MOVEA (2.381,.,1.375)
ISN 0020 CALL LINEA (2.155.0.1.25)
ISN 0021 CALL LINEA (2.165.-2.91.25)
ISN 0022 CALL DRAW (CIR (1))
ISN 0023 CALL LINEA (2c38,-2�,-1.375)O
ISN 0024 CALL DRAW (CIR (2))
ISN 0025 CALL LINEA (2.165,-2&,1.25)
FIGURE 4.12 Computer program to construct velocity fields
MAIN OS/350 -ORTRAN H EXTENDED
ISN 0026 CALL MOVEA (2.381-2',1 .375)
ISN 0027 CALL LINEA (2,381.o0.,1.375)
ISN 0028 CALL MOVEA (2.16590.-1,25)
ISN 0029 CALL LINEA (2.165,-2s,-1.25)
ISN 0030 CALL MOVEA (2.165,0,9-1.25)
ISN 0031 CALL DASH (.075*.075)
ISN 0032 CALL LINEA (.974390*s-5625)
ISN 0033 CALL DRAW (CIR(4))
ISN 0034 CALL LINEA (2*1b5*0. .1.25)
ISN 0035 CALL MOVEA (.g743.0.o56251
ISN 0036 CALL LINEA (.9743-2e,.5625)
ISN 0037 CALL LINEA (2.1659-2*91.25)
ISN 0038 CALL MOVEA (.9743-2.,.5625)
ISN 0039 CALL DRAW (CIR(3))
ISN 0040 CALL LINEA (2.165-2.t-1*25)
ISN 0041 CALL MOVEA (*9743-2,-5525
ISN 0042 CALL LINEA (.9743.0.,-.5625)
ISN 0043 CALL NDASH
ISN 0044 CALL MOVEA (09, 0.,0,)
ISN 0045 CALL LINEA (0.-,01Cs)
C VELOCITY FIELD PLOTTING
C X1FAST-DRAW=VD(DATA)0. DX FAST-DRAW=DYD
C Y FAST-DRAW=-XD(DATA)* DY FAST-DRAW=-DXD
C Z FAST-DRAW=ED(DATA)v DZ FAST-DRAW=DZD
C MUST HAVE 1000001 CARD AT END OF DATA
C READ DATA CARDS
ISN 0046 ITOTAL=O
ISN 0047 DO 5' I=19.0
ISN 0048 READ(S,100) Y.ZX(I),R(I) ,THETA(I),UX(I),VR(I),WT(I),DYDZ
ISN 0049 100 FORMAT(8X.10F6.2)
ISN 0050 IF(X(I),EQ,.0) GO TO 6
ISN 0052 I TOTAL=I TOTAL+ I
ISN 0053 RATIO(I)=l.-R(I)/63.5
ISN 0054 X1=X(I)
ISN 0055 DX=UX(I)
C SCALE CONVERTS MM TO INCH
ISN 0056 SCALE1=0.0394
ISN 0057 XI=KI*SCALEI
ISN 0058 Y=Y*SCALEI
ISN 0059 Z=Z*SCALE1
ISN 0060 CALL MOVEA (Y,-XIZ)
C SCALE2 CONVERTS MM TO INCH AND SCALES VELOCITY
ISN 0061 SCALE2=0.005
ISN 0062 DX=)X*SCALE2
ISN 0063 DY=DY*SCALE2
ISN 0064 DZ=DZ*SCALE2
FIGURE 4.12 - continued
LEVEL 2,1 4 JAN 75 )
IDATE 76*251/15
MAIN OS/360 -ORTRAN H EXTENDED
ISN 0065
ISN
ISN ISN
ISN
ISN ISN
ISN
ISN ISN
ISN ISN
ISN ISN
ISN
ISN
ISN
ISN ISN
ISN ISN
ISN
0066 0067
0068 0069 0071 0072 0073
0074 0075
0076 0077 0078
0079
0080 0081 0082 0083
0084
0085 0086 0087
ISN 0088 ISN 0089 ISN 0090 ISN 0091 ISN 0092 ISN 0093 ISN 0094 ISN 0095 ISN 0096 ISN 0097 ISN 0098 ISN 0099 ISN 0100 ISN 0101 ISN 0102 ISN 0103 ISN 0104 ISN 0105
FIGURE 4.12 -
CALL LINE (DV,-DXDZ)
C THIS PORTION WILL CONSTRUCT ARROWHEADS ON THE VECTORS WHICH ARE IN
C THE PLANE OF VECTOR-Z AXIS, 30% OF VECTOR LENGTH, AND 30 DEGREE
C INCLUDED ANGLE. TANGENTOF 1/2 ANGLE{ 15) IS** 0.26795
A=DK*D X+D Z*D Z
B=SQRT (A*DX*DX+A*Al
C=O
IF(3.EQ.O.O0) C=1.
VUI=A/( B+C)
VU2= DX*DY/(B+Cj
VU3=-DY*DZ/( B+C)
RI=-.3*DY
R 2=- * 3* (-D X)
R3=-.3*DZ
D=0.3*( SQR.T(A+DX*DX) ) *0,26795
P1X=RI+VUI *D P1Y=R2+VU2 D PIZ=R3+VU3*D
P2X=RI+VU1 *(-D,)
P2Y=R2 +VU2 *(-D) P2Z=R3+VU3*(-D)
CALL LINE (PIX.PIY,PIZ)
CALL MOVE (-PlX,-PIYl,-PIZ)
CALL LINE (P2X9P2YvP2Z)
5 CONTINUE
C THIS S--TION WILL PLOT 5 CUTS AND A VIEW OF ALL PLANE VELOCITY VECTORS
C FOR BOT+ THE R-THETA PLANE AND THE X-R PLANE
C DRAW PLOT OF R-THETA CUTS
6 CALL FACT (1.0)
CALL CLEAR. (4,5.9)
CALL XY
CALL ORIG (18.6915.2)
CALL TXSIZ (0.0875)
CALL TXPLT (-1.6-1.844,0.+1lO0&2@*)
CALL TXPLT (-1 .6,-l,266,0., 1,
CALL TXPLT (-1.6,-0.588,0.,+I,'0.4@*)
CALL TXPLT (-1.6,1.156,0,9+I1,C*2@') CALL TXPLT (-.6,1.73490.*, Y/R@") CALL TXPLT (-1.6,2.312.0.i+1,0.4�) CALL TXPLT (0.*02.70,O.,Oi'X=2-10@) CALL TXPLT (3.0,2.70,0.,09'X=10-18@') CALL TXPLT (6*0,2.7090#s0*'X=18--26')
CALL. TXPLT (0.0,-030,0.,0,'X=26-34@*)"
CALL TXPLT (3,0,-0*30,09.090X=34-42@0).
CALL TXPLT (-6.0,-030q,0,sX=ALL@').
DO 10 J=192
continued
LEVEL 2",1 ( JAN 75 )
DATE 7,6,251/15
MAIN OS/360 =ORTRAN H EXTENDED
.ISN ISN ISN
ISN ISN
ISN ISN
ISN
ISN
ISN ISN
ISN I SN
ISN
ISN
ISN
ISN
ISN I SN
ISN ISN
[SN
ISN
ISN
ISN
ISN
ISN ISN
ISN ISN
0106 0107 0108 0109 0110 0111
0112 0113 0114 0115
0115 0117 0118 0119 0120 0121
0122 0123
0125 0127 0129
0131 0133
0134 0135
0136 0137 0138 0139 0140
ISN 0141 ISN 0142 ISN 0143 ISN 0145 [SN 0146 ISN 0147 ISN 0145 ISN 0149
ISN 0150 ISN 0151
ISN 0152
FIGURE 4.12 -
DO 20 1=1,3
XOR IG=18.6+30*( I-1) YOR I G= 5.2-3.0*( J-1)
CALL ORIG (XCRIG.YORIG)
CALL MOVEAC-1.40.iJ CALL LINEA (-1.4,0.)
CALL LINEA (1*Iv0.,i
CAL" LINEA (1.4,0.1)
CALL MOVEA (0.,091)
CALL LINEA (0.0.)
CALL TXPLT (-l.�5.-0.1O.,0+l,*-2Oa)*)
CALL TXPLT O.,-O.1 0�90'0@,)
CALL TXPLT (07,-0-I,0,v0'THETA l)
CALL TXPLT' (1,4-01,Cv.,-1, 20@.6)
UPLIMX=8.*I+2,+(J-I)} 24.
LOLIMX=UPL IMX-8.
C DRAW VECTORS IN PLOT OF R-THETA CUTS
DO 30 K=I.ITOTAL
IF(THETA(K).LT�(-20.).OR.THETA(K)�GT.20�) GO TO 30
IF(RATIO(K).LT.O.OR.RATIO(K).GT.0.0�5) GO TO 30
IF(X(K).LT.2.OR.X(K).GT.42.) GO TO 30
IF(I*JEQ6) GO TO 31
IF(K(K).LT.LOLIMXOR.X(K).GT.UPLIMX) GO TO 30
31 CONTINUE
C MULTIPLY RATIO AND THETA TIMES SCALE FACTORS TO =IT SPACE
VERTD=RAT[O( KJ*5.78 HORIZD=THETA(K) * 0.07
C MULTIPLY VR AND WT TIMES A SCALE FACTOR TO ADJUST VECTORSTO PLOT SCALE
SCALE 3=0.045
VERTV=-VR(.K) *SCALE3 HORI ZV=WT(K) *SCALE3
CALL MOVEA (HORIZDVERTD) CALL LINE (HORIZVIVERTV)
C DRAW ARROWHEADS ON VECTORS OF 30% VECTOR LENGTH AND 30 DEGREE
C INCLUDED ANGLE. TANGENT OF 1/2 ANGLE(15) IS 0.26795
C=SQRT(VERTV*VERTV+HORIZV*HORIZV)
B=0
IF(C.EQOO) B=.
VUI=VERTV/(Cff3)
VU2=-HGRIZV/(C+)
RI=-O .3*HORI ZV R2=-0. 3'VERTV
D=0. 3*0.26795*C
PIANG=RI+VUI *D
P lRAT=R2+VU2*D
P2ANG=RI +VUI *(,-D)
continued
LEVEL 2,1 ( JAN 75 )
DATE 75o251/15
OS/360 =0.RTRAN H EXTENDED
ISN 0153 P2RAT=R2+VU2*(-D)
ISN 0154 CALL LINE (PIANG,.PIRAT)
ISN 0155 CALL MOVEI (-PIANG,-PIRAT)
ISN 0156 CALL LINEI(P2ANGvP2RAT)
ISN 0157 30 CONTINUE
ISN 0158 20 CONTINUE
ISN 0159 10 CONTINUE
C DRAW PLOT OF X-R CUTS
ISN 0160 CALL ORIG (18.6,5.2)
ISN 0161 CALL TXPLT (-1�6,-1.844,0o,+1,'0,2Z')
ISN 0162 CALL TXPLT (-16v-l266,0, +,*Y/R@f)
ISN 0163 CALL TXPLT (-1.6,-0*688,0**+19l0*4@*)
ISN 0164 CALL. TXPLT t-1.6,1.156,0,,+1,@0,28')
ISN 0165 CALL TXPLT (-I .6,1,734,0,*,1,'Y/R@')
ISN 0166 CALL TXPLT (-1.6,2*312,0*,+I,'0*4i')
ISN 0167 CALL TXPLT (O,0O2,70,O,,9 THETA=20-12Q0)
ISN 0168 CALL TXPLT (3,0,2,70,0,,v9THETA=I2-4@')
ISN 0169 CAL. TXPLT (6,O2.70,0.,0, 'THETA=4-(-4)@')
ISN 0170 CALL TXPLT (00,-030,0,0,'THETA=-4)--12)@i)
ISN 0171 CALL TXPLT (3.0,-O,30,0-,O,'THETA=(-12)-(-20)@')
ISN 0172 CALL TXPLT (690,-03009099THETA=ALL@')
ISN 0173 DO 40 J=1,2
ISN 0174 DO 50 1-1.3
ISN 0175 XORIG=1896+3,0*(I-1)
ISN 0176 YORIG= 5,2-3.0*(J-1)
ISN 0177 CALL ORIG (XORIG,YORIG)
ISN 0178 CALL MOVEA(-1 ,4,O01 )
ISN 0179 CALL LINEA (-1.4,0.)
ISN 0180 CAL. LINEA (194,0e)
ISN 0181 CALL LINEA (1e4,091)
ISN 0182 CALL MOVEA (0*,0.1)
ISN 0183 CALL LINEA (0**0.)
ISN 0184 CALL TXPLT (-.4,-0,C0,1,08e
ISN 0185 CALL TXPLT (09,-0,l*0e,0,'25@0)
ISN 0186 CALL TXPLT (0.7,-0.1,0.,0,'X'@g)
ISN 0187 CALL. TXPLT (1.4,-0*1,0-,-1,'50e)
ISN 0188 UPLIMT=20,-(I-1)*8.-(J-1)*24.
ISN 0189 LOLIMT=UPLIMT-8ISN 0190 DXORIG=XcR;IG-1.4
ISN 0191 CALL ORIG (DXJRIGYORIG)
C DRAW VECTORS IN PLJT OF X-R CUTS
ISN 0192 DO 60 K=1,ITOTAL
ISN 0193 IF(THETA(K),LT(-2C.) ORTHETA(K).GT.20,) GO TJ 60
ISN 0195 IF(RATIO(K).LT.0.cJRRATIO(K),GT.0.45) GO TO 60
ISN 0197 IF(X(K)eLT.OGRX(K).GT,45,) GO TO 60
ISN 0199 IF(I*JEG.6) GO TO 61
FIGURE 4.12 - continued
MAIN
DATE 76.251/15,
LEVEL 2.1 (
JA N 75 )
|
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